SOLUTION: Keller performed the work below to express the polynomial in factored form: r(x) = x4 - 8x2 - 9 r(x) = (x2 + 1)(x2 - 9) (x) = (x + 1)(x - 1)(x + 3)(x - 3) Explain

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Keller performed the work below to express the polynomial in factored form: r(x) = x4 - 8x2 - 9 r(x) = (x2 + 1)(x2 - 9) (x) = (x + 1)(x - 1)(x + 3)(x - 3) Explain      Log On


   

Question 1182006: Keller performed the work below to express the polynomial in factored form:
r(x) = x4 - 8x2 - 9
r(x) = (x2 + 1)(x2 - 9)
(x) = (x + 1)(x - 1)(x + 3)(x - 3)
Explain the error he made and complete the factorization correctly.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
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to express the polynomial in factored form:
r(x) = x4 - 8x2 - 9
r(x) = (x2 + 1)(x2 - 9)
(x) = (x + 1)(x - 1)(x + 3)(x - 3)
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x%5E4-8x%5E2-9

-9 and +1 ?
%28x%5E2-9%29%28x%5E2%2B1%29

Recognize the Difference Of Squares. That is the factor containing the -9; not the other factor.

%28x-3%29%28x%2B3%29%28x%5E2%2B1%29

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Keller performed the work below to express the polynomial in factored form:
r(x) = x4 - 8x2 - 9
r(x) = (x2 + 1)(x2 - 9)
(x) = (x + 1)(x - 1)(x + 3)(x - 3)
Explain the error he made and complete the factorization correctly.
x + 1 and x - 1 are NOT factors of x2 + 1. 

Having said that, can you now provide the correct factorization?