Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

Tutors Answer Your Questions about Polynomials-and-rational-expressions (FREE)

Question 571432: 7a/a-b / 4b/a+b = This problen is 7a over a-b divided by 4b over a+b
Answer by stanbon(48516)

(Show Source):

You can put this solution on YOUR website!
7a over a-b divided by 4b over a+b
-----
Invert the denominator and multiply:
[7a/(a-b)] * [(a+b)/(4b)]
------
= [7a(a+b)]/[4b(a-b)]
===========================
Cheers,
Stan H.
===============

Question 571111: factor completely
7x^2-7x^2y-28x+28xy
Answer by KMST(578)

(Show Source):

You can put this solution on YOUR website!
We can find common factors in groups of terms, and see what we end up with:
7x%5E2-7x%5E2y-28x%2B28xy=%287x%5E2-7x%5E2y%29%2B%28-28x%2B28xy%29=7x%5E2%281-y%29%2B28x%28-1%2By%29

7x%5E2-7x%5E2y-28x%2B28xy=%287x%5E2-7x%5E2y%29%2B%28-28x%2B28xy%29=7x%5E2%281-y%29%2B28x%28-1%2By%29

If both factors in brackets were exactly the same, we would be finding a common factor again. We can fix that, because
%28-1%29%28-1%2By%29=%281-y%29

7x%5E2%281-y%29%2B28x%28-1%2By%29=7x%5E2%28-1%29%28-1%2By%29%2B28x%28-1%2By%29=%28%28-1%297x%5E2%2B28x%29%28-1%2By%29

and we can write that in more elegant ways, and even factor out a

%28%28-1%297x%5E2%2B28x%29%28-1%2By%29=%28-7x%5E2%2B28x%29%28y-1%29=-7%28x%5E2-4%29%28y-1%29

Because

, it can be factored too, to get to the full factorization.
-7%28x%5E2-4%29%28y-1%29=-7%28x%2B2%29%28x-2%29%28y-1%29

Question 570916: What is the difference in these two questions and how do I do them?
Describe the mathematic process of canceling like factors when working with rational expressions. Demonstrate this with an example. And explain in your own words how factoring is used to solve quadratic equations. Demonstrate the process with an example. Please help this is late and I am so lost
Found 2 solutions by harsh.9119, richard1234:
Answer by harsh.9119(1)   (Show Source):
You can put this solution on YOUR website!
x^2+12x+35=0
i.e. x^2+7x+5x+35=0
i.e. (x+7)(x+5)=0
i.e. x=-7 && x=-5

Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
Canceling like factors is similar to canceling common factors in a fraction such as 15/24. Pretty straightforward, as long as you cancel the factors correctly.

Factoring helps solve quadratics, as you don't have to use the quadratic formula. If x^2 + bx + c = 0 factors to (x-p)(x-q) = 0, then right away you know that the roots are p and q. However, not all quadratics factor nicely, and you almost have to "recognize" instantly if a quadratic is factorable (by being able to factor the constant term), otherwise the method is useless.

For example, consider the quadratic . Since 35 = 5*7 and 5+7 = 12, you could factor it like

(check to make sure the coefficients are the same upon expanding). By the zero-product rule, the roots are -5 and -7.

Factoring quadratics with a leading term other than 1 uses a slightly different method; look in your textbook or online for examples.

Question 571134: factor completely
7x^2-7x^2y-28x+28xy
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
7x^2-7x^2y-28x+28xy
7x^2(1-y)-28x(1-y)
(1-y)(7x^2-28x)
(1-y)*7x(x-4)
7x(x-4)(1-y)

Question 571036: For a polynomial f(x) with real coefficients having given the degree and zeros.
Degree 4; zeros:-2-5i; 5 multiplicity 2
Answer by reviewermath(39)   (Show Source):
You can put this solution on YOUR website!
The conjugate of -2-5i is -2+5i. We first get a quadratic equation having -2-5i and -2+5i as roots.
sum = (-2-5i) + (-2+5i) = -4
product = (-2-5i)(-2+5i) = 29

The quadratic equation is
Next, we get the quadratic equation having 5 as a double root.
The quadratic equation is
We multiply the two quadratic equations to get the polynomial of degree 4.

Answer:

Question 571074: Could someone give me an example or two. All this talk about rational expressions has me so lost. This is why I have yet to post my work on this topic. I understand that in math we learn about fractions I get them, my daughter tells me that a fraction is just a funny looking expressions and they are just tools for writing down that one number that is divided by another here is where I get lost even more. I believe that I am making it even harder than it is with all of the rules for working with fractions, I have been told a million times that they are basically all grounded in this math stuff, however I believe that with a little more time they will start to make sense I hope. If I am lost someone help me out please. From what I have learned so far a rational expressions is very much like a fraction, except they usually represent ratios of variable expressions, instead of just ratios of numbers. I believe that the rules for working with rational expressions are basically the same as the rules that I understand for fractions is this correct? I believe all this is even more confusing I hate that this is going to take some practice.
Answer by Edwin McCravy(6932)   (Show Source):
You can put this solution on YOUR website!
Try this site:
http://tutorial.math.lamar.edu/Classes/Alg/RationalExpressions.aspx
Also try these youtube videos:
http://www.youtube.com/watch?v=L1KD-C0lWsY
http://www.youtube.com/watch?v=f7WjJ_Zg7VY&feature=related
http://www.youtube.com/watch?v=xPNwdbmhmuA&feature=related
Edwin

Question 571062: a^2-12a+32=0 The solutions are?
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
solution (8,4)

Question 571045: Factor each polynomial completely. a^2-14a+24
Answer by nyc_function(2626)   (Show Source):
You can put this solution on YOUR website!
a^2 - 14a + 24 =
Ask yourself: What two numbers multiplied together will yield 24 but when added will produce the middle term which is -14.

How about -12 and -2?

Answer: (a - 12) (a - 2)

Question 571038: 8xy^4 + 27x^4y factor completely, if prime state
Answer by nyc_function(2626)   (Show Source):
You can put this solution on YOUR website!
8xy^4 + 27x^4y =

xy(8y^3 + 27x^3) =

We now use the sum of cubes to factor the binomial in the parentheses.

In the parentheses, we apply the formula

(a^3 + b^3) = (a + b)(a^2 - 2b + b^2)

Then (8y^3 + 27x^3) becomes (2y + 3x)(4y^2 - 6xy + b^2).

Final answer = xy(2y + 3x)(4y^2 - 6xy + b^2)

Question 570930: Please explain how to solve: a rectangular pool 20 feet wide and 60ft long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 sq ft, how wide is the walkway?
Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
Please explain how to solve: a rectangular pool 20 feet wide and 60ft long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 sq ft, how wide is the walkway?
-----------------
w = the width of the walkway
The outside dimensions are 20 + 2w by 60 + 2w
------------
The area inside the walkway is (20 + 2w)*(60 + 2w)
The area of the pool is 20*60 = 1200 sq ft
-----
516 = (20 + 2w)*(60 + 2w) - 1200
Solve for w

Question 570907: what natural can replace B to make perfect square trinomial
64X^2+BX+16
Answer by josmiceli(6778)   (Show Source):
You can put this solution on YOUR website!

The quadratic formula to find roots is:

To make a perfect square,
must be zero

-----------
If

-----------
If

-----------
can be replaced with either or
Here are plots of the 2 alternatives:

Question 570890: factor out polynomial GCF
j(k-5)-10(k-5)
Answer by Edwin McCravy(6932)   (Show Source):
You can put this solution on YOUR website!
If it were jA-10A then you would factor out the red A, and it would leave the green j and the green -10 to go in black parentheses like this: A(j-10) Therefore since it's j(k-5)-10(k-5) then you likewise factor out the red (k-5), and it leaves the green j and the green -10 to go in black parentheses like this: (k-5)(j-10) ----- The only difference is that A doesn't take up as much space as (k-5). One thing to learn in algebra is how to treat big chunks of algebra the same way as you treat little chunks of algebra. Edwin

Question 570892: factor out GCF
40x^7y^8+72x^2y^6+72x^4y^3
Answer by maa.veera@gmail.com(3)   (Show Source):
You can put this solution on YOUR website!
40x^7y^8+72x^2y^6+72x^4y^3
8*5*x^2*x^5*y^3*y^5 + 8*9*x^2*y^3*y^3 + 8*9*x^2*x^2*y^3
8x^2y^3(x^5y^5+ 9y^3+9x^2)

Question 570889: factor out the polynomial gcf
x(y+10)-z(y+10)
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
factor out the polynomial gcf
x(y+10)-z(y+10)
----
gcf = (y+10)
---
Factored Form: (y+10)(x-z)
===============================
cheers,
Stan H.

Question 570887: factor by factoring out gcf 5c-20
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
factor by factoring out gcf 5c-20
gcf = 5
---
Factor form: 5(c-4)
========================
cheers,
Stan H.

Question 570781: How do I factor a trinomial? I have seen many examples of this problems but i still dont understand, the problem is, -6s2 - s - 5. Can you help me?
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
-6s2 - s - 5
The coffecient of s^2=-6
The coefficient of third term is -5
Multiply both you get 30
You have to split this number (30)into two parts such that when you add them you get the coefficient of the middle term which is -1
Factorize 30
the prime factors are 2*3*5
From the factors you get, combine the factors. For example 2& 3 , & 5
2*3=6
& 5
5-6=-1
That is the coefficient of the middle term
So you can now write
-6s^2-6s+5s-5
-6s(s-1)+5(s-1)
(s-1)(5-6s)
m.ananth@hotmail.ca

Question 570679: Find a 4th degree polynomial equation with integer coefficients which has
two irrational roots, one of which is 2+3, and two imaginary
roots, one of which is 3-2i.

Answer by Edwin McCravy(6932)   (Show Source):
You can put this solution on YOUR website!
Find a 4th degree polynomial equation with integer coefficients which has two irrational roots, one of which is 2+3, and two imaginary roots, one of which is 3-2i. In order to have integer coefficients if a polynomial equation has the irrational root , it must also have its conjugate . Similarly if it has an imaginary root C+Di as a root, it must also have its conjugate C-Di as a solution. So, since it must have integer coefficients, and 2+3 is a root, then 2-3 is also a root. And since it has 3-2i as a root, 3+2i is also a root. So if it were solved we would have to end up with these four solutions: x = 2+3, x = 2-3, x = 3-2i, x = 3+2i So before that we would have had x - (2+3) = 0, x - (2-3) = 0, x - (3-2i) = 0, x - (3+2i) = 0 And before that we would have had: x - 2 - 3 = 0, x - 2 + 3 = 0, x - 3 + 2i = 0, x - 3 - 2i = 0 And before that we would have had: (x - 2 - 3)(x - 2 + 3)(x - 3 + 2i)(x - 3 - 2i) = 0 Now we must multiply that out and collect terms to get our fourth degree polynomial equation: It will be easier if we group the first two terms in each parentheses: [(x-2) - 3][(x-2) + 3][(x-3) + 2i][(x-3) - 2i] = 0 The first two bracket expressions are like multiplying (A+B)(A-B)=A²-B², and the last two bracketed expressions are too: [(x-2)² - 9·5][(x-3)² - 4i²] = 0 [(x-2)² - 45][(x-3)² - 4(-1)] = 0 [(x-2)² - 45][(x-3)² + 4] = 0 [x²-4x+4 - 45][x²-6x+9 + 4] = 0 (x² - 4x - 41)(x² - 6x + 13) = 0 x⁴ - 6x³ + 13x² - 4x³ + 24x² - 52x - 41x² + 246x - 533 = 0 x⁴ - 10x³ - 4x² + 194x - 533 = 0 Edwin

Question 570659: how do you get the answer to (2x+6)²
Answer by Edwin McCravy(6932)   (Show Source):
You can put this solution on YOUR website!
(2x+6)² To square something, you multiply it by itself, so write it down twice: (2x+6)(2x+6) and multiply using FOIL: (2x)(2x) + (2x)(6) + (6)(2x) + (6)(5) 4x² + 12x + 12x + 36 4x² + 24x + 36 Edwin

Question 570414: x^6 - 4x^3 + 1 = ?
Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

What a cute little sixth degree trinomial. Is there a part of the instruction "Please try to ask your question clearly and fully so that it MAKES SENSE. We are not mind readers. We do not have your textbook in front of us. All we know is what you wrote." that you don't understand?

John

My calculator said it, I believe it, that settles it

Question 570157: How to factorize x^3-8x^2+11x+20? Please provide me detailed explanation.

Answer by AnlytcPhil(1116)   (Show Source):
You can put this solution on YOUR website!
Factor: x³ - 8x² + 11x + 20 If there are any rational zeros they must be ± divisors of 20, which are ±1, ±2, ±4, ±5, ±10, ±20. We try the easiest, 1, using synthetic division: 1| 1 -8 11 20 | 1 -7 4 1 -7 4 24 No that gives remainder 24, not 0 We try the next easiest, -1: -1| 1 -8 11 20 | -1 9 -20 1 -9 20 0 That gives remainder 0, so (x + 1) is a factor of the polynomial. Therefore (x + 1)(x² - 9x + 20) is a partial factorization, but not a complete factorization, because the binomial in the second parentheses can be factored, and the final factorization is: (x + 1)(x - 5)(x - 4) Edwin

Question 570101: Can you please help me simplify this equation: . Can I also get step by step on how to do it.
Answer by Maths68(1140)   (Show Source):
You can put this solution on YOUR website!
=
=
=
=
=

Question 569949: can you describe how to do 24x^3 - 46x^2 + 20x = 0

Answer by nyc_function(2626)   (Show Source):
You can put this solution on YOUR website!
How to do what? What exactly do you need done with this polynomial? There are many things that can be done. Get my point?

Question 569954: can you describe how to do x^2 - 9x - 22 = 0

Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!

Start with the given equation.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

Question 569613: solve b^2-10b+16=0
Answer by Maths68(1140)   (Show Source):
You can put this solution on YOUR website!
b^2-10b+16=0
b^2-8b-2b+16=0
b(b-8)-2(b-8)=0
(b-8)(b-2)=0
b-8=0 or b-2=0
b=8 or b=2

Question 569352: 10r^2/40r
Answer by IWork4Dessert(57)   (Show Source):
You can put this solution on YOUR website!
This is a monomial, or a number where the denominator(bottom part) doesn't have any addition/subtraction/multiplication/division. When you have a binomial--for example, 10r^2/40r+8r^2--you can't just cancel out the elements of the top and bottom halves of the equation, but with a monomial you can.
All you need to do is expand the equation now:
10 x r x r / 40 x r
Now you cancel out the like numbers and terms. You can see that 10 divides evenly into 40, so you can cancel them out to get:
r x r / 4 x r
You can also cancel out a pair of the r's.
r / 4
Your answer is r/4.

Question 568499: Here is another subtracting rational expressions problem that is giving me some trouble. I am fine until I have factored and try to combine numerators. The minus sign throws me off. I am not sure what I am doing wrong, but I think it might be the order in which I am doing things. Do I multiply each numerator separately before combining, or maybe I'm switching the positives and negatives wrong. I need to know the correct order in which combine the numerators. One of my problems is:
3x+1/x-1-x-1/x-3+x+1/x^2-4x+3=
Answer by KMST(578)   (Show Source):
You can put this solution on YOUR website!
I assume your problem was:
(3x+1)/(x-1)-(x-1)/(x-3)+(x+1)/(x^2-4x+3)= The long horizontal fraction lines come with invisible brackets enclosing the expressions in the numerator and the denominator. If you can only use slanted lines, and you fail to write all those brackets, it means something different. Then, math geeks misunderstand you and so do most calculators. I've seen people report wrong results at work because they forgot to type those brackets into the calculator.
Minus signs give everyone trouble, but I have tricks that help me deal with them. It is an unconventional way of working, and I found it is safer for me not to show it openly too often, but I’ll let you in on my secret. Minus signs are dangerous and should not be allowed to wander around unescorted. If we could keep them trapped within brackets, it would be better. I see your minus sign as part of an invisible (-1):
==
=
=
=

I do not usually write out the meaning of the minus signs so explicitly (too much work and too controversial), but I make an exception here for your benefit. I wrote some of those minus signs the way I see them in my mind. I believe that minus signs belong to the number that follows them, which may not always be visible to everyone, like that (-1) I am making visible for you. And of course I believe that there is no such thing as subtraction, it’s just adding a negative number. Unfortunately we are all indoctrinated to believe in subtraction since we are very young.

Question 568757: how would you find the lowest common denominator for the following rational expressions: 8/y squared minus 5y, and -2/y squared minus 2y minus 15. I am having trouble grasping the concept of factoring rational expressions ,and any help would be greatly appreciated.
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
how would you find the lowest common denominator for the following rational expressions:
8/y squared minus 5y, and -2/y squared minus 2y minus 15.
----
8/(y^2-5y) and -2/(y^2-2y-15)
-----
Factor:
8/[y(y-5)] and -2/[(y-5)(y+3)]
----
Lowest Common Denominator: (y(y-5)(y+3))
==============================================
Cheers,
Stan H.
==============

Question 568740: what is the zero product property for f(x)=2x^3+6x^2+4x
Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

First set the function equal to zero to make a polynomial equation. Then factor the polynomial. There is one monomial factor and two binomial factors. Each of the factors can be zero and satisfy the equation.

John

My calculator said it, I believe it, that settles it

Question 568725: How do I factor this problem completly? (75a^3-12a)
Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

Take out a factor of , then what remains will be the difference of two squares.

John

My calculator said it, I believe it, that settles it

Question 568639: show all work. Bob’s Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 5x3 – 9x2 – 2x – 3. The shop estimates their costs for that quarter to be given by x2 + 4x + 7. For the second quarter, find and simplify a polynomial that will represent their profit. Note: Profit = Revenue - Costs
Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

Since

Just substitute:

Then distribute the minus sign across the right-hand set of parentheses and collect like terms.

John

My calculator said it, I believe it, that settles it

Question 568507: (a + b - c)(a + b + c)
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Hint:

(a + b - c)(a + b + c) = a(a + b + c) + b(a + b + c) - c(a + b + c)

Question 568486: I am having a little difficulty with subtracting rational expressions. Specifically, it is the part after the factoring is complete and the numerators are being combined. The minus sign is throwing me off. I know that the signs to the right of the minus sign change, but I'm having a little trouble with the combining. One of my problems is as follows:
2x-3/x+5-x^2-4x-19/x^2+8x+15

Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
Use parentheses so you can see what you are doing.
-------------------
(2x-3)/(x+5)-(x^2-4x-19)/(x^2+8x+15)
----
Factor:
= (2x-3)/(x+5) - (x^2-4x-19)/[(x+5)(x+3)]
-----------------
LCD = (x+5)(x+3)
-----
Rewrite both factors with denominator = LCD
----
= [(x+3)(2x-3)]/LCD - [x^2-4x-19]/LCD
-------
Combine the numerators over the LCD:
---
= [2x^2+3x-9-x^2+4x+19]/LCD
----------------
Simplify:
= [x^2+7x+10]/LCD
----
Factor:
= [(x+5)(x+2)]/[(x+5)(x+3)]
----
Cancel the common factor:
= (x+2)/(x+3)
=======================
Cheers,
Stan H.
=============

Question 568377: The sides of a triangle have lengths of (3x-5),(x-7) and (7x+12). What is the perimeter of the triangle in terms of X?
Answer by bucky(2097)   (Show Source):
You can put this solution on YOUR website!
You are given that the three sides of the triangle have lengths of 3x-5 and x-7 and 7x+12.
.
The perimeter of a polygon in plane geometry is found by adding the lengths of all the sides. Therefore, the perimeter of this triangle is found by adding the three lengths of the sides. This can be done as follows:
.
Perimeter = 3x-5 + x-7 + 7x+12
.
Algebraically add together all the terms containing x. This involves adding 3x+x+7x and the sum of 3+1+7 = 11. So combining the terms containing x results in an answer of 11x.
.
Then algebraically add together all the constants. This involves adding -5 -7 and +12. Notice that when you add these the result is zero since -5 plus -7 equals -12 and when added to +12 cancels out to zero.
.
This means that the perimeter of this triangle is 11x + 0 or just 11x.
.
I hope that this helps you to better understand how to find the perimeter of plane figures when each of the sides is given by an algebraic expression.
.

Question 568369: I need help solving this (y+1)(3y^2+3y)
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
(y+1)(3y^2+3y)
(y+1)*3y(y+1)

Question 568349: Please help me find the x-intercepts and the y-intercepts for F(x)= -x^2 + 2x + 24
Thank you
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
find the x-intercepts and the y-intercepts for F(x)= -x^2 + 2x + 24
-----
y-intercept = ?
Let x = 0 ; then y = 24
---------------
x-intercept = ?
Let y = 0 and solve for "x":
-x^2+2x+24 = 0
---
x^2-2x-24 =0
(x-6)(x+4) = 0
x = 6 or x = -4
==================
Cheers,
Stan H.
==================

Question 568336: Problem is F(x) = -(x-2)^2 -7 I need to find the vertex , line of symmetry, maximum/minimum value I am not sure if I am doing these problems right can anyone help me with a step by step? Thanks
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
The equation is in vertex form.
Notice that is x = 2, y will be -7
Notice that any other value of x will result
in y being a value more negative than -7
----------------------------------------------
F(x) = -(x-2)^2 -7 I need to
find the vertex (2,-7)
-----
line of symmetry:: x = 2
---------
maximum/minimum value::: max = -7
==================
Cheers,
Stan H.

Question 568309: i really dont get how to factor the polynomial can you help[ me plz.
Answer by TutorDelphia(189)   (Show Source):
You can put this solution on YOUR website!

the first step is to see if there is something we can factor out from each term.
If I rewrite everything like this, its more clear

or if I do a prime factorization of each number like this:

So each term has 2*2*b*b which is 4b^2
so I need to factor out 4b^2 from each term
4b^2*(3b^2+9b-5)
and we can factor further if need be but you can probably stop here.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=141 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.479057014506319, -3.47905701450632. Here's your graph:

Question 568283: ax+3=2x-5y
Solve for x.
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
ax+3=2x-5y
---
ax - 2x = -5y-3
---
(a-2)x = -(5y+3)
----
x = -(5y+3)/(a-2)
=========================
Cheers,
Stan H.

Question 568247: show all work. Consider that the age, x, of a unicorn in human equivalent years can be given by the formula f(x) = - 0.003518x^4 + 0.087326x^3 – 1.3367x^2 + 12.46x + 2.914. When a unicorn is 2.5 years old, what is its age in human equivalent years? What about when it is 12 years old?
Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
Just plug in x = 2.5 to find f(2.5), and simplify (preferably with a calculator). Similarly, find f(12).

Question 568029: 2x^+7x-30
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
2x^2+7x-30 = 0
-----
Quadratic formula:
x = [-7 +- sqrt(49 - 4*2*-30)]/4
------
x = [-7 +- sqrt(269)]/4
---
x = [-7 +- 16.40]/4
========================
Cheers,
Stan H.

Question 567942: Could you please help me express the following problem in the simplest form. Can you please show your work so I can see how you got the answer. Thanks!!
3
_________
a + 2

plus
8
_________
a - 5

Answer by Earlsdon(6098)   (Show Source):
You can put this solution on YOUR website!
Simplify:
Add the two fractions. First get the common denominator by multiplying the denominators of the two fractions.

Now add the fractions:
Simplify this.
==

Question 567426: The discriminant of the equation 8x^2-9x+5=0 is
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
From we can see that , , and

Start with the discriminant formula.

Plug in , , and

Square to get

Multiply to get

Subtract from to get

So the discriminant is

Since the discriminant is less than zero, this means that there are two complex solutions.

In other words, there are no real solutions.

Question 567518: Factor
8r^3-27
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!

Start with the given expression.

Rewrite as . Rewrite as .

Now factor by using the difference of cubes formula. Remember the difference of cubes formula is

Multiply

-----------------------------------
Answer:
So factors to .

In other words,