Answers Algebra II Polynomial Operations — TestQuestion 16

16

QuizMultiple Choice

Polynomial Operations — Test

Question 16 • Algebra II

What is the completely factored form of p to the 4th power minus 16 ?

Answer

A

open paren p minus 2 close paren times open paren p minus 2 close paren times open paren p minus 2 close paren times open paren p minus 2 close paren

B

open paren p minus 2 close paren times open paren p plus 2 close paren times open paren p squared plus 2 p plus 4 close paren

C

open paren p minus 2 close paren times open paren p plus 2 close paren times open paren p squared plus 4 close paren

Explanation

Use the difference of squares: p⁴ − 16 = (p² − 4)(p² + 4). Then factor p² − 4 = (p − 2)(p + 2), giving (p − 2)(p + 2)(p² + 4), which is choice C.

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