Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.4 Factoring Polynomials - A.4 Assess Your Understanding - Page A40: 109

Answer

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

Work Step by Step

First, for the polynomial $1 - 8x^2 - 9x^4$, we write $$ 1 - 8x^2 - 9x^4=-(9x^4+8x^2-1)=-(9x^4+9x^2-x^2-1) .$$ By grouping the first two terms and the second two terms and then taking common factors, we have $$-(9x^4+9x^2-x^2-1) =-(9x^2(x^2+1)-(x^2+1))\\ =-(x^2+1)(9x^2-1) .$$ The polynomial $x^2+1$ can not be factored because it is prime. The remaining terms can be factored as follows: $$9x^2-1=(3x-1)(3x+1)$$ where we recognized the difference of two squares $(a-b)(a+b)=a^2-b^2$.
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