1. ## Factoring Polynomials Help

So I have to do a review in my Precalculus textbook from Algebra 2 and their are these 3 questions that I just don't seem to understand. I have the answer in the back of the book but I want to know how to get to the answer.

Questions are:

(x+2)^2 - 5(x+2) - Answer is - (x+2)(x-3)

3(x^2+10x+25) - 4(x+5) - Answer is (x+5)(3x+11)

I Just don't undestand how they got to those answers.

2. Originally Posted by Kros
So I have to do a review in my Precalculus textbook from Algebra 2 and their are these 3 questions that I just don't seem to understand. I have the answer in the back of the book but I want to know how to get to the answer.

Questions are:

(x+2)^2 - 5(x+2) - Answer is - (x+2)(x-3)

3(x^2+10x+25) - 4(x+5) - Answer is (x+5)(3x+11)

I Just don't undestand how they got to those answers.
1) $\displaystyle 1 -8x^2 - 9x^4 = -9x^4 - 8x + 1$

We need two numbers that multiply to become $\displaystyle -9$ and add to become $\displaystyle -8$. They are $\displaystyle -9$ and $\displaystyle 1$.

$\displaystyle -9x^2 - 8x + 1 = -9x^4 - 9x^2 + 1x^2 + 1$

$\displaystyle = -9x^2(x^2 + 1) + 1(x^2 + 1)$

$\displaystyle = (x^2 + 1)(1 - 9x^2)$

$\displaystyle = (x^2 + 1)[1^2 - (3x)^2]$

$\displaystyle = (x^2 + 1)(1 - 3x)(1 + 3x)$.

Double check the answer you have been given.

2) $\displaystyle (x + 2)^2 - 5(x + 2)$

Take out a common factor of $\displaystyle x + 2$

$\displaystyle = (x + 2)(x + 2 - 5)$

$\displaystyle = (x + 2)(x - 3)$.

3) $\displaystyle 3(x^2+10x+25) - 4(x+5) = 3(x + 5)^2 - 4(x + 5)$

$\displaystyle = (x + 5)[3(x + 5) - 4]$

$\displaystyle = (x + 5)(3x + 15 - 4)$

$\displaystyle = (x + 5)(3x + 11)$.