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Tutors Answer Your Questions about Polynomials-and-rational-expressions (FREE)
Question 283688: The way that we write numbers is based on the powers of 10. We know that ;
10^0=1
10^1=10
10^2=100
10^3=1000 etc.
we also know that 2 times 10^1=20
Using this information write the number 6734 as a polynomial in the form. Answer by richwmiller(3948) (Show Source):
Question 283663: In a triangle one angle is 23 degrees more than the smallest angle the third angle is 10 degrees more than the sum of the other two angles find the measurement of each angle
I can not figure out how to write this problem out my book has nothing like it and I cant find it online PLEASE HELP Answer by oberobic(528) (Show Source):
You can put this solution on YOUR website!The triangle has 3 angles: a, b, and c.
We know that a + b + c = 180 degrees because all triangles have 180 degrees.
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We'll pick 'a' as the smallest angle.
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b = a + 23 :: given
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c = a+b+10 :: given
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So, it seems we have 3 unknowns and not enough equations to solve them.
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But let's think about it.
.
We have
a = a
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b = a+23
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c = a+b+10
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for 'c', substitute b=a+23
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c = a + (a+23) +10
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a + b + c = 180,
so...
a + (a+23) + (a+(a+23)+10) = 180
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4a + 56 = 180
4a = 124
a = 31
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b = a +23
b = 31+23 = 54
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c = a + b + 10
c = 31 + 54 + 10 = 95
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Do they add up to 180?
31 + 54 + 95 = 180
Correct.
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The three angles are: 31, 54, and 95.
.
Done.
Question 283541: x^2-x/1-x^2 Answer by checkley77(9435) (Show Source):
Question 283596: Plz show work for (3-7i)(3-7i) or (3 − 7i)^2. Thanks! Answer by jim_thompson5910(14954) (Show Source):
Question 283564: Factor out the GCF in each expression.
(x - 2)x -(x - 2)
Factor out the GCF in each expression, then factor out the opposite of the GCF.
12u^5v^6 + 18u^2^v3 - 15u^4v^5 Answer by user_dude2008(940) (Show Source):
You can put this solution on YOUR website!(x - 2)x -(x - 2) = (x-2)(x-1)
12u^5v^6 + 18u^2^v3 - 15u^4v^5 = 3u^2v^3(4u^3v^3+6-5u^2v^2)
12u^5v^6 + 18u^2^v3 - 15u^4v^5 = -3u^2v^3(-4u^3v^3-6+5u^2v^2)
Question 283568: use the rational root theorem to list all possible rational roots of the polynomial equation x3+x2+-7x-4=0 do not find the actual roots.
How do i do this problem Answer by jim_thompson5910(14954) (Show Source):
You can put this solution on YOUR website!Any rational zero can be found through this equation
 where p and q are the factors of the last and first coefficients
So let's list the factors of -4 (the last coefficient):
Now let's list the factors of 1 (the first coefficient):
Now let's divide each factor of the last coefficient by each factor of the first coefficient
Now simplify
These are all the distinct rational zeros of the function that could occur
Note: Not all of these values are actual roots.
Question 283559: Find a polynomial for the perimeter and the area.
one side is = b+2
the other side is= b
The perimeter is______(simplify your answer. do not factor)
The area is_______(simplify your answer. do not factor) Answer by checkley77(9435) (Show Source):
You can put this solution on YOUR website!one side is = b+2
the other side is= b
Perimeter=2L+2W
PERIMETER=2(B+2)+2B
PERIMETER=2B+4+2B
PERIMETER=4B+4 OR 4(B+1) ANS.
AREA=LW
AREA=B(B+2) ANS.
Question 283537: 4p-8p squared Answer by richwmiller(3948) (Show Source):
Question 283490: Simplify 4k^2+k-3-3k^2-5k+6 Answer by jim_thompson5910(14954) (Show Source):
Question 283463: Write each polynomial in standard form. Then name each polynomial based on its degree and number of terms.
9z^2-11z^2+5z-5
Thank you Answer by richwmiller(3948) (Show Source):
Question 283475: Two times the reciprocal of an integer, plus 4 times the reciprocal of 3 times the integer is 1/3. find the integer. Answer by oberobic(528) (Show Source):
You can put this solution on YOUR website!The reciprocal of x is 1/x.
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'3x' is the common denominator, so multiply through by 3x to cancel the denominators.
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Checking...
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.

Correct
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The integer is x=10.
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Done
Question 283425: It takes machine A twice as long to produce 10,000 bolts as it takes machine B. Together they do the job in 8 hours. How long will it take each machine to produce 5,000 bolts if each works separately? Answer by richwmiller(3948) (Show Source):
Question 283419: A pharmacist has 600mL of an 8% sucrose solution. If he lets some of the water evaporate until he has a 12% solution, will he have enough left to fill 3 prescriptions needing 150mL each? Explain your answer using complete sentences. Answer by richwmiller(3948) (Show Source):
Question 283339: Is the product of a binomial always a trinomial? Explain with examples. Answer by nabla(459) (Show Source):
You can put this solution on YOUR website!Is the question this:
Is the product of two binomials always a trinomial?
If not, disregard this solution.
Consider:
(a+b)(a-b)=a^2-ab+ab-b^2=a^2-b^2. This is a binomial. Hence, it is not always true that the product of two binomials is a trinomial.
However, it is true in many other cases:
(a+b)^2=a^2+2ab+b^2
Question 283359: If x^2 = 3x + 4, then x^5 is equal to:
(A) 3x + 4 (B) 13x + 12 (C) 51x + 52 (D) 205x + 204 (E) 819x + 820 Found 2 solutions by nabla, richwmiller: Answer by nabla(459) (Show Source): Answer by richwmiller(3948) (Show Source):
You can put this solution on YOUR website!d)205x+204
The other tutor found it one way.
I solved for x
x=-1 or 4
Then I went through the possibles answers to see which one fit.
Question 283146: Factor completely
x^2 - 16x + 64 Found 2 solutions by irenevecchio44, richwmiller: Answer by irenevecchio44(1) (Show Source): Answer by richwmiller(3948) (Show Source):
Question 283385: Not sure how to get the exponent to a positive.
(7.1*10 neg 7)(8.6*10 neg5) Answer by Alan3354(8326) (Show Source):
You can put this solution on YOUR website!7.1E-7 * 8.6E-5
= 7.1*8.6E-12
= 61.06E-12
= 6.106E-11 or

Moving the exponent to the denominator to make it positive doesn't accomplish anything.
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This is 0.00000000006106
It's  which is rounded to 5 places
6.106E-11 is the best expression of it.
Question 283379: how do I factor completely:
4a^2 -4a -48 Answer by richwmiller(3948) (Show Source):
You can put this solution on YOUR website!right away you can see that you can factor 4
4*(a^2-a-12)
now we have 1 and 12
so we need factors of twelve with a difference of one
1 12 11
2 6 4
3 4 1
4 3 1
we are repeating and the only match is 3 and 4
the larger number must be negative
(a-4)*(a+3)
so now we have 4*(a-4)*(a+3)
Question 283374: How do I factor an expression?
Answer by richwmiller(3948) (Show Source):
Question 283207: Use long division or synthetic division to find
the quotient and remainder of
(x3 - 9x2 + 15x + 25) ÷ (x - 5)
Answer by mananth(583) (Show Source):
You can put this solution on YOUR website!x-5) x^3-9x^2+15x+25 ( x^2
___x^3-5x^2
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-4x*2+15x ( -4x
-4x^2+20x
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-5x+25 ( -5
-5x+25
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Quotient = x^2-4x-5
Question 283300: the product of two consecutive positive odd integers is one less than three times their sum. find the integers. Answer by mananth(583) (Show Source):
You can put this solution on YOUR website!let the number be x
the second number will be x+2
the product will be x(x+2)
three times the sum less 1 = 3(x+x+2)-1
x(x+2)=3(2x+2)-1
x^2+2x=6x+6-1
x^2+2x-6x=+6-1
x^2-4x=+5
x^2-4x-5=0
x^2-5x+x-5=0
x(x-5)+1(x-5)=0
(x+1)(x-5)=0
x=-1 or 5
So 5 & 7 are the numbers
Question 283202: how do i find the polynomial for the shaded area of a rectangle tha the withis 14y-5 and the highth is 6y and in the rectangle theres a nother rectangle with the with of 3yplus 5 and the highth is 3y Found 2 solutions by Alan3354, kela1616: Answer by Alan3354(8326) (Show Source):
You can put this solution on YOUR website!The larger rectangle's area is (14y-5)*6y
The inside rectangle's area is (3y+5)*3y
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The excluded area is the difference.
= 
=
Answer by kela1616(2) (Show Source):
Question 283311: Susan can do a certain job in 5 hours. Kim can do the same job in 3 hours. Working together, how many hours would they need to do the job? Answer by richwmiller(3948) (Show Source):
You can put this solution on YOUR website!x/5+x/3=1
3x+5x=15
8x=15
x=15/8
x=1 7/8 hours
x/5=15/8/5=3/8 of the job
x/3=15/8/3=5/8 of the job
Sue does 3/8 and Kim does 5/8 of the job
Question 283303: two cars leave an intersection, one car travels north the other east. When the car traveling north had gone 12 miles the distance between the cars was 8 miles more than the distance traveled by the car heading east. how far had the eastbound car traveled? Found 2 solutions by oberobic, richwmiller: Answer by oberobic(528) (Show Source):
You can put this solution on YOUR website!This is an interesting application of the Pythagorean Theorem.
The car traveling north can be viewed as going up the y-axis 12 units.
The car going east can be be viewed as going to the right along the x-axis.
It has traveled 'd' miles.
The diagonal from that connects the two cars is the hypotenuse of a right triangle.
It's length is d+8, which is given.
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12^2 + d^2 = (d+8)^2
144 + d^2 = d^2 +16d + 64
subtract d^2 from both sides
144 = 16d + 64
subtract 64 from both sides
80 = 16d
divide both sides by 16
5 = d
d = 5
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Check to ensure diagonal 'c' is 5+8 =13.
c^2 = 12^2 + 5^2
c^2 = 144 + 25
c^2 = 169
So, c = 13
Correct.
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Answer:
The eastbound car has travelled 5 miles.
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Done.
Answer by richwmiller(3948) (Show Source):
Question 283296: frank can type a report in 4 hours and james takes 7 hours. how long will it take the two of them typing together? Found 2 solutions by oberobic, richwmiller: Answer by oberobic(528) (Show Source):
You can put this solution on YOUR website!Frank works at a rate of 1/4 job per hr.
James works at a rate of 1/7 job per hr.
It takes them 'x' hours to do one entire job.
x*(1/4) + x*(1/7) = 1
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x/4 + x/7 = 1
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7x + 4x = 28
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11x = 28
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x = 28/11 = 2.54545
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check by seeing how much of the job each does in 2.54545 hr
2.54545*1/4 = .6363
2.54545*1/7 = .3636
.6363+.3636 = .9999, which is pretty close to 1 whole job
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Answer:
Working together it takes them 2.54545 hrs.
Or about 2 hr 33 min
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Done
Answer by richwmiller(3948) (Show Source):
You can put this solution on YOUR website!This problem might make math sense but practically how do you divide up the job of typing a report?
x/4+x/7=1
7x+4x=28
11x=28
x=28/11
x=2 6/11
Question 283253: i need to know what is A=pi*r^2 Answer by richwmiller(3948) (Show Source):
Question 283220: Factor each binomial completely given that the second binomial is a factor of the first binomial.
2x^3 - 5x^2 - x - 6; x-3 Answer by richwmiller(3948) (Show Source):
Question 283116: x-7/x+9=4/7
What is solution(s) for x? Answer by checkley77(9435) (Show Source):
You can put this solution on YOUR website!x-7/x+9=4/7
(X*X-7)/X=4/7-9
(X^2-7)/X=(4-9*7)/7
(X^2-7)/X=(4-63)/7
(X^2-7)/X=-59/7 CROSS MULTIPLY.
7(X^2-7)=-59X
7X^2-49+59X=0
7X^2+59X-49=0

x=(-59+-sqrt[59^2-4*7*-49])/2*7
x=(-59+-sqrt[3,481+1,372])/14
x=(-59+-sqrt4,853])/14
x=(-59+-69.66)/14
x=(-59+69.66)/14
x=-10.66/14
x=.76 ans.
x=(-59-69.66)/14
x=-128.66/14
x=-9.19 ans.
Question 283197: The product of 2 consecutive intergers is 41 more than their sum. find the intergers Answer by oberobic(528) (Show Source):
You can put this solution on YOUR website!Two consecutive numbers can be defined as x and y, but a better choice is x and x+1.
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The product of the two numbers is: x(x+1). We are told this 41 more than the sum.
The sum of the two numbers is: x + (x+1).
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So the equation we need to solve is:
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x(x+1) = x+(x+1)+41
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x^2 +x = 2x + 42
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subtract 2x from both sides
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x^2 +x -2x = 2x-2x + 42
x^2 -x = 42
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subtract 42 from both sides
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x^2 -x -42 = 42-42 = 0
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factor
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(x-7)(x+6) = 0
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x = 7 or -6
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We have to check both solutions by substituting these values into the equation.
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7(7+1) = 7+(7+1)+41 ??
7*8 =56
7+8 + 41=56
Correct
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-6(-6+1)=-6+(-6+1)+41 ??
36 -6 = -6 -6 + 42 ??
30 = 30
Correct.
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Answer the consecutive integers are either 7 and 8 OR -6 and -5.
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Done
Question 283115: z-4/z+2=1/6
Solution for z = ? Found 2 solutions by richwmiller, unlockmath: Answer by richwmiller(3948) (Show Source): Answer by unlockmath(450) (Show Source):
You can put this solution on YOUR website!Hello,
Let's first remove the fractions by multiplying by 6z. This will give us:
6z^2-24+12z=z Now subtract z from both sides to get:
6z^2+11z-24=0 Now use the quadratic Form to solve:
 Plug in the values:
z = (-11 +- sqrt( 121+576))/(12) Simplify to:
z=-11+-sqrt697/12
There you go.
RJ
www.math-unlock.com
Question 283187: what are the possible number of positive,negative,and imaginary roots of f(x)=x3-2x2-3x-20 Answer by richwmiller(3948) (Show Source):
Question 283165: solve using the principles of 0 products
b(b + 16)(b + 3)=0 Answer by richwmiller(3948) (Show Source):
Question 283144: factor out the largest common factor...y^8 - 16y^5 Answer by richwmiller(3948) (Show Source):
Question 283095: Could you explain, step by step, how to solve the following equation?
Let f(x) = | 3 – 7x |. Find all x for which f(x) > 10
Thank you.
Cynthia Answer by dabanfield(606) (Show Source):
You can put this solution on YOUR website!Let f(x) = | 3 – 7x |. Find all x for which f(x) > 10
We have |3-7x| > 10 when either 1.) 3-7x > 10 or when 2.) -(3-7x) > 10.
1.) 3-7x > 10
7x < 3-10
7x < -7
x < -1
2.) -(3-7x) > 10
7x-3 > 10
7x > 10+3
7x > 13
x > 13/7
The solution set for f(x) is all real numbers x where x < -1 or x > 13/7.
Question 283078: The sum of the solutions of the equation x^4 + 2x^3 − 13x^2 − 14x + 24 = 0
Is
(A) −2 (B) −1 (C) 0 (D) 1 (E) 2
Answer by richwmiller(3948) (Show Source):
Question 282927: I am not sure this problem is a Polynomial,any help you can offer would be great. Sorry the -2 is under the 1st set of parenthsis & -4 is under the 2nd set. Thanks
4+ (-3x+4)=(-2x+6)+24
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-2 -4
Answer by nyc_function(545) (Show Source):
You can put this solution on YOUR website!Do you mean the following?
[4 + (-3x + 4)]/-2 = [(-2x+6)+ 24]/-4
Is this what you are trying to simplify?
Simplify numerator as step one.
(-3x + 8)/-2 = (-2x + 30)/-4
Multiply both sides of the equation by the LCD -4. This multiplication process will remove the fractions from both sides of the fractional equation.
(-2)(-3x + 8) = -2x + 30
6x - 16 = -2x + 30
Can you solve for x now?
Question 282957: Factor by grouping...8a^3 - 2a^2 + 12a - 3 Answer by richwmiller(3948) (Show Source):
Question 282842: if p and q are the zeroes of a polynomial ax2+bx+c then evaluate p-q Answer by Edwin McCravy(3640) (Show Source):
Question 282914: 1. x2-2x-24 2. x2+3x-10 (two problems)x2 is little 2 after an uphigh on x.. (how to do problems) Complete the square for the following quadratic polynomials (that is, express in the form(x + _)2 + _ where you fill in the blanks with numbers). (x+ _)2 is little 2 after ). Answer by jim_thompson5910(14954) (Show Source):
You can put this solution on YOUR website!I'll do the first one to show you how to do these problems.
 Start with the given expression.
Take half of the  coefficient  to get  . In other words,  .
Now square  to get  . In other words,
 Now add and subtract  . Make sure to place this after the "x" term. Notice how  . So the expression is not changed.
 Group the first three terms.
 Factor  to get  .
 Combine like terms.
So after completing the square,  transforms to  .
In other words,  .
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