Factoring Polynomials Completely — Quiz

Question 15 • Mathematics III

What is the completely factored form of x to the 4th power plus 8 x squared minus 9 ?

Answer

open paren x plus 1 close paren times open paren x plus 1 close paren times open paren x plus 3 close paren times open paren x plus 3 close paren

open paren x plus 1 close paren times open paren x minus 1 close paren times open paren x plus 3 close paren times open paren x plus 3 close paren

open paren x squared minus 1 close paren times open paren x plus 3 close paren times open paren x minus 3 close paren

open paren x plus 1 close paren times open paren x minus 1 close paren times open paren x squared plus 9 close paren

Explanation

Treat x² as a single variable: x⁴ + 8x² − 9 = (x²)² + 8(x²) − 9. This factors as (x² + 9)(x² − 1), and the difference of squares gives (x² + 9)(x + 1)(x − 1). So the completely factored form is choice D, (x + 1)(x − 1)(x² + 9).

AI-written and checked against the verified answer.

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