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Math Help - Factoring Polynomials Help

  1. #1
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    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:

    1-8x^2-9x^4 - Answer is -(3x-1)(3x+1)(x^2-1)

    (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.
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    Quote Originally Posted by Kros View Post
    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:

    1-8x^2-9x^4 - Answer is -(3x-1)(3x+1)(x^2-1)

    (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) 1 -8x^2 - 9x^4 = -9x^4 - 8x + 1

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

    -9x^2 - 8x + 1 = -9x^4 - 9x^2 + 1x^2 + 1

     = -9x^2(x^2 + 1) + 1(x^2 + 1)

     = (x^2 + 1)(1 - 9x^2)

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

     = (x^2 + 1)(1 - 3x)(1 + 3x).

    Double check the answer you have been given.


    2) (x + 2)^2 - 5(x + 2)

    Take out a common factor of x + 2

     = (x + 2)(x + 2 - 5)

     = (x + 2)(x - 3).


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

     = (x + 5)[3(x + 5) - 4]

     = (x + 5)(3x + 15 - 4)

     = (x + 5)(3x + 11).
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