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

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 Algebra: Polynomials, rational expressions and equations Solvers Lessons Answers archive Quiz In Depth

4/5 + 7/8 = s/20

the solution is s= ??

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4/5 + 7/8 = s/20

32/40 + 7/8 = s/20

32/40 + 35/40 = s/20

(32 + 35)/40 = s/20

67/40 = s/20

67*20 = 40s

1340 = 40s

1340/40 = s

s = 1340/40

s = 67/2 <--- Answer as a fraction

s = 33.5 <--- Answer as a decimal

Solve for k in k/k+1=3/k^2-k-2
A. k=-1 and k=2
B. k=-1 and k=3
C. k=3
D. k=-1
Thank you!

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Solve for k in k/k+1=3/k^2-k-2
factor denominator on right side of =
k /(k+1) = 3 / (k-2)*(k+1)
multiply both sides of = by (k-2)*(k+1)
k*(k-2) = 3
k^2 -2k -3 = 0
factor the above equation and we get
(k-3)*(k+1) = 0
to solve set (k-3) = 0 and (k+1) = 0
solutions are k = 3 and k = -1

Question 759106: I need help please.
Factor and simplify 2x^2+5x+3/2x^2-x-6.
A. x^2+5x+3/x^2-x-6
B. 5x+3/-x-6
C. x+1/x-2
D. It is already fully simplified.

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Factor and simplify 2x^2+5x+3/2x^2-x-6
numerator factors into (2x+3)*(x+1)
denominator factors into (2x+3)*(x-2)
so we have (2x+3)*(x+1) / (2x+3)*(x-2)
then cancel (2x+3) from numerator and denominator and we have
(x+1) / (x-2) and the answer is C

Question 758980: If ax^3+bx^2+x-6 has (x+2) as a factor and leaves a remainder 4 when divided by (x-2).find the value of a and b?
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Use synthetic division with a divisor of into a dividend of to get . Then do the same thing with a divisor of to get . Solve the 2X2 system. See Purple Math Synthetic Division if you need a refresher.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 759002: The area of a rectangle is 96ft square.
The width is 4 less than the length.
What is the perimeter?
I am having trouble coming up with a formula for questions similar to this.
L*W = 96, and L-4=W is all I got.

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The area of a rectangle is 96ft square.
The width is 4 less than the length.
What is the perimeter?
I am having trouble coming up with a formula for questions similar to this.
L*W = 96, and L-4=W is all I got.
----------------
That's all you need.
Sub for W in the 1st eqn
L*W = 96
L*(L-4) = 96
L^2 - 4L - 96 = 0
(L - 12)*(L + 8) = 0
L = 12
--------
W = 8
----
You could have tried factors of 96 and gotten 8 by 12, too.
Perimeter = 40

Question 758867: Factor x³ + 7x² - x - 7 completely
Answer by Edwin McCravy(8999)   (Show Source):
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x³ + 7x² - x - 7

Factor x² out of the first two terms and -1 out of the last two terms:

x²(x + 7) - 1(x + 7)

Factor (x + 7) of of the two terms:

(x + 7)(x² - 1)

Factor the second parentheses as the difference of two squares:

(x + 7)(x - 1)(x + 1)

Edwin

Question 758852: -x^7-9x^6-52x^5=
You can put this solution on YOUR website!
-x^7-9x^6-52x^5
---------------------
= -x^5[x^2 + 9x + 52]
-----
Cheers,
Stan H.
=========

Question 758618: Determine the roots of the equation x^2+4x=45 can you help me in the first steps
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x^2 + 4x = 45
Change the side of the 45
changing its sign
x^2 + 4x - 45= 0
Now you need to find two numbers
that multiply together to give you -45
and add together to give you +4
5 x 9 = 45
Keep the larger number positive
and make the smaller on negative
-5 x +9 = -45
-5 + 9 = 4
(x - 5)(x + 9) = 0
Hope this helps.
:-)

Question 758370: Write each area measurement in the specified unit:
288 in.^2; square feet
54 yd^2; square feet
48 ft^2; square inches
108 ft^2; square yards

Found 2 solutions by k_pardo, MathLover1:
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They weren't supposed to be negative, so sorry. I meant the "-" as a way to list each question.

Question 758299: Here is my question:
when p(x) is divided by x-1 the remainder is 1, and when divided by (x-2)(x-3) the remainder is 5. find remainder when P(X) is divided by (x-1)(x-2)(x-3).
here is part of my work:
let the quotient be Q(x), and let the remainder be ax+b
P(x)=(x-1)(x-2)(x-3)Q(X)+ax+b
P(1)=a*1+b=1 then a+b=1 (1)
thanks

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is cubic (degree=3) polynomial.
When you divide by the remainder polynomial could have degree 2, 1, or 0, so you should start with for a remainder.

That gives you the sytem

--> and
--> , so
-->
Then,
--> --> -->
--> -->
and finally
--> --> -->
The remainder when is divided by is

There are infinite possibilities for , as there are for . simplest corresponds to
In that case,

Question 758165: find the value of 1/(root3-root2-1) correct upto 3 decimals if root2=1.414 and root6=2.45.
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find the value of
correct up to 3 decimals if and
We know the square root of 3 = square root of 6/ sqrt of 2
therefore
= = = -1.468

Question 758051: 2x^3+5x^2-x-22 x=-3
Found 2 solutions by jim_thompson5910, stanbon:
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2x^3+5x^2-x-22

2(-3)^3+5(-3)^2-(-3)-22 ... plug in x = -3

2(-27)+5(9)-(-3)-22

-54+45+3-22

-9+3-22

-6-22

-28

So 2x^3+5x^2-x-22 = -28 when x = -3

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2x^3+5x^2-x-22 x=-3
-----
2x^3 + 5x^2 -x - 19 = 0
----
I graphed the cubic and found only one Real solution at x = 1.587
The other solution must be complex numbers.
----------
Cheers,
Stan H.

( u-v/8v) + (6u - 3v/ 8v)

You can put this solution on YOUR website!
I assume it is:
+
Each fraction has the same denominator so we can write it

combine like terms

Question 758052: The given equation is either linear or equivalent to a linear equation. Solve the equation.
z/6=((3/10)z)+2
So far I have tried ...
0=((3/10)z)+2-(z/6)
0=z+2-(z/6)
-12=z-z
I've also tried ...
z=((3/10)z)+12
0=((3/10)z)+12-z
-12=((3/10)z)-z
-12/(-7/10)=((-7/10)z)/(-7/10)
-120/-7=z

Found 2 solutions by stanbon, oscargut:
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z/6=((3/10)z)+2
----
Just a suggestion::
When you have fractions, get rid of them:
---
Multiply thru by 60 to get:
10z = 6*(3z) + 120
----
10z = 18z + 120
---
6z = -120
---
z = -20
====================
Cheers,
Stan H.

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Solution
z/6=((3/10)z)+2
Multiply by 6
z = (18/10)z+12
(18/10-1)z = -12
(8/10)z = -12
z = -12(10)/8
z = -15
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Question 758016: How to convert 2.4 *10^-4 to standard notation?

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If you need more help with math questions/assignments/tests
You can ask me more using this e-mail (mthman@gmail.com) or you can visit my site:
http://mathshelp-online.com/
(Payment is using paypal)

Question 757768: Find the product of zeros of -2x2 +kx+6 .
Found 3 solutions by solver91311, Edwin McCravy, josgarithmetic:
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Which you should recognize as a conjugate pair the product of which is the difference of two squares:

John

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

Answer by Edwin McCravy(8999)   (Show Source):
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-2x² + kx + 6

If r1 and r2 are the zeros of

ax² + bx + c

then sum of zeros = r1+r2 =
and product of zeros = r1r·sub>2 =

-2x² + kx + 6

a = -2, b = k, c = 6

and product of zeros =  =  = -3

Edwin

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Using r and s for the zeros,

Better simplifying, multiplying each by :

The product:

Question 757724: Factor: x^2-x-45
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Factor: x^2-x-45
---------------------
x = [1 +- sqrt[1-4*-45]/2
---
x = [1 +- sqrt(181)]/2
---------------
x = (1+sqrt(181))/2 or x = (1-sqrt(181))/2
==============
Factor: (x-(1+sqrt(181)2/2)(x-(1-sqrt(181))/2)
==============
Cheers,
Stan H.,

Question 757705: Perform the indicated operation. Be sure the answer is reduced.
x+1/x-8 minus x/8-x =
A. 2x+1/x-8
B. 2x-1/x-8
C. 2x+1/x+8

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The trick here is to remember that

So the second term of your sum is actually and your entire sum becomes:

which is equivalent to:

All that is left is simply adding the two numerators.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 757650: Solve the following exponential equation 5^x=8
X=____

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Solve the following exponential equation 5^x=8
--------------
Don't post the "X = _________ " It serves no purpose.
------------

x*log(5) = log(8)
x = log(8)/log(5) the base change formula

Question 757651: Solve the equation
In x+ In (x+2)=2
X=___

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In x+ In (x+2)=2
------
It's ln, for natural log

Can you finish it?

Question 757610: For what value of k, -4 is a zero of the polynomial x2 – x – (2k + 2)?
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if

........plug in

as you can see, is a zero of the polynomial

Question 757576: write an expression that represents the product of 3 less than x and five more than twice x
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(x - 3)(2x + 5)
Hope this helps.
:-)

Question 757473: How do you factor things like 2xy^2 or 5xy^2
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How do you factor things like 2xy^2 or 5xy^2
----------
They're only 1 term, not much to factor.
2xy^2 = 2*x*y*y
No reason to do that.

Question 757423: Examples of real life problems that requires rational expressions to solve ?
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What is giving you difficulty with this question?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 757326: A rectangle is 10n centimeters long by (n + 6) centimeters wide. Write its area as a polynomial.
Found 2 solutions by Cromlix, LearnWithMajor:
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Area of a rectangle = length x width
= 10n (n + 6)
= 10n^2 + 60n
Hope this helps.
:-)

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Area of a rectangle is equal to length times width
A = l*w
l = 10n centimeters
w = n+6 centimeters
A = 10n(n+6) square centimeters
square centimeters

Question 757276: Simplify the polynomials
((7x^3y^2-21x^2y+35x^3y^4)/7x^2y);neither x or y is equal to 0

Question 757031: Choose the real solutions of the system:
x = (y^2) + -9 and x - 4y - 12 = 0
I tried using the substitution method but I keep getting stuck!

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x = (y^2) + -9 and x - 4y - 12 = 0
from second equation. Substitute into the first equation.

You should no longer be stuck. The lefthand side is factorable.

-----------
Just a little bit of review:

If you find some square trinomial as any general and you want to factor it, try thinking of it as
So you are looking for two numbers, h and k, so that hk=b and h+k=a.
What you do is look for all the two-number factorizations for b, and find which ones give you a sum of a. We then test each combination until we find something that works. There is a somewhat more analytical way also, but the search and test method is usually enough.

Question 757017: I'm wondering how to solve this. I don't understand how to get the rest of the roots.
Solve:
(c^3) + (c^2) - 7c -3 = 0, given root -3

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If is a root of , then must be a factor of

Use either polynomial long division (Purple Math Polynomial Long Division) to derive the other (quadratic) factor by dividing by , or by using synthetic division ((Purple Math Synthetic Division) to find the coefficients of the quadratic factor. Either way, solve the resulting quadratic equation. The roots will be irrational, so you will not be able to solve by factoring; use Completing the Square or the Quadratic Formula.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

2x3-5x2-4x+3

You can put this solution on YOUR website!
x + 1 divides into 2x^3 - 5x^2 - 4x + 3
Leaving 2x^2 - 7x + 3
(2x - 1)(x - 3)
so factorised:
(2x^2 - 1)(x - 3)(x + 1)
Hope this helps
:-)

Question 756852: 3x^2-15x+16
You can put this solution on YOUR website!
3x^2-15x+16
------
x = [15 +- sqrt(225-4*3*16)]/6
-------
x = [15 +- sqrt(33)]/6
=====================
Cheers,
Stan H.

Question 756798: How do I find the real zero of a polynomial function fx=-9(x-8)(x-1).
I put it in my calculator and it solved the problem for -72. But I do not know the amount of real zeros or how to find them if there are any.

Found 2 solutions by MathLover1, Alan3354:
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.....to find the real zero of a polynomial function set
...since you have completely factored, use zero product rule to find solutions
...since , the product will be equal to zero if or
if =>
if =>
so, you have two real zeros
let see them on a graph:

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How do I find the real zero of a polynomial function fx=-9(x-8)(x-1).
-9(x-8)(x-1) = 0
(x-8)(x-1) = 0
Either (x-8) = 0 --> x = 8
or (x-1) = 0 --> x = 1

Question 756666:

Question 756718: So, my text for this week is about factoring trinomials by grouping and factoring with FOIL in reverse. As well as the Difference of Two Squares, Perfect Square Trinomials and the Sum and Difference of Two Cubes.
I need a discussion question that will trigger a discussion—that is, so there is no single correct answer to the question. Anyone have any ideas? I am stumped on this one.

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So, my text for this week is about factoring trinomials by grouping and factoring with FOIL in reverse. As well as the Difference of Two Squares, Perfect Square Trinomials and the Sum and Difference of Two Cubes.
I need a discussion question that will trigger a discussion—that is, so there is no single correct answer to the question. Anyone have any ideas? I am stumped on this one.
------------
Look at Purplemath.com, or similar sites.

Question 756687: how can i solve 2/5a multipy 6/7a^2
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how can i solve 2/5a multipy 6/7a^2
-----
(2/5)a * (6/7)a^2
-----
= (2*6/5*7)a^3
----
= (12/35) a^3
===============
Cheers,
Stan H.
===============

Question 756634: x3 (x2+4x+1)
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x3 (x2+4x+1)
--------------
Do you have a question?

Question 756596: I want to check my answer to see if I done this problem correctly.
Use the ac method to solve this expression:
35x^2 - 2x - 1
My answer resulted in 35x^2 - 2x -1 factors to (5x - 1)(7x + 1)

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looks good to me.
Bob

Question 756549: 9 - x^2 divided by x - 3 for all x < -3
A) 3x
B) x+3
C) x-3
D) -x +3
E) -x -3

Question 756543: If f(x) = 2x + 1 and g(x) = (x – 1)/2 , then f(g(x)) =
So, I know what to do... Basic plug and chug. I also know that the answer is X, I just don't know how to get to the answer.
I plug in g(x)...
f(x) = 2(x-1/2)+1, distribute... (2x-2+1)/2, combine like terms... (2x-1)/2.
Now that's where I get stuck. I don't know how to get to x, unless I did my math wrong. How do I get to x?