Question

I need some help with Polynomial Long Division.

Answer 1

1. Let \[f(x)=27x^5-33x^4-21x^3\]

4.The volume of a rectangular prism is represented by the function x^3 + 11x^2 + 20x - 32. The width of the box is x - 1 while the height is x + 8. Find the expression representing the length of the box.

@phi
Can you walk me through theses two problems please.

Answer 2

1. let f(x)=27x^5-33x^4-21x^3 and g(x)=3x^2 find \[\frac{ f(x) }{ g(x) }\]

Answer 3

Question 4

well start by dividing the volume by the product of the 2 know lengths...

\[(x -1)(x+8) = x^2 +7x - 8 \]

or you can divide the volume by (x -1) then divide the quotient by (x + 8)

or you can use a little insight..

you know 2 of the linear factors... and since the Volume is a cubic, it means there is only 1 more linear factor...

the product of the 2 known factors has a constant of -8

the Volume has a constant of -32

so -8 * ? = -32

the last factor is (x + ?) which will be the length

hope this helps

Answer 4

you can use long division or synthetic division
If you want to see how it is done, see
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/dividing_polynomials/v/polynomial-division

Answer 5

and the other question can be broken into parts

\[\frac{f(x)}{g(x)} = \frac{27x^5}{2x^2}- \frac{33x^4}{3x^2} - \frac{21x^3}{3x^2}\]

simplify each part

Answer 6

oops 1st fraction should have a coefficient in the denominator of 3... not 2

Answer 7

I understand how to do number 1 now, THANKS! When it comes to any math I really need a better explanation than FLVS gives, my teacher don't do a good job of calling me back then I get stuck and behind.
I still don't get #4 though.

Answer 8

wait never mind I see what you were saying. Thank you, I do have one more question though.
It says divide \[28x^3+42x^2-35x \] by 7x
do I do the same thing as #1

Answer 9

ok...here is the simple version of No 4

I've divided the volume by x - 1

to eliminate x^3 in the volume I need to multiply (x -1) by x^2

so I end up subtracting x^3 - x^2 from the volume... leaving

12x^2 then I bring down the 20x..

so next (x-1) is multiplied by 12x to eliminate 12x^2

this is repeated



there is no remainder so you know the volume can be written as

\[(x -1)(x^2 + 12x + 32)\]

you can find the length by factoring the quadratic.... you already know one of the factors is (x + 8)... so find the other... which will be the length

hope it helps