Operating with Polynomials — Test

Question 11 • Mathematics III

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

Answer

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

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

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

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

Explanation

Use the difference of squares: p⁴ − 16 = (p²)² − 4² = (p² − 4)(p² + 4). Factor p² − 4 again as (p − 2)(p + 2), giving (p − 2)(p + 2)(p² + 4). This is choice B; p² + 4 does not factor further over the integers.

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