How do you factor z^3 + 2z^2 - 16z - 32z3+2z2−16z−32 by grouping?

1 Answer
EZ as pi
Jun 13, 2016

(z + 2)(z + 4)(z - 4)(z+2)(z+4)(z−4)

Explanation:

There are 4 terms, so group them into two group of two - make sure there is a PLUS sign between the groups.

(z^3 + 2z^2) + (-16z -32) " common factor from each pair"(z3+2z2)+(−16z−32) common factor from each pair
=z^2(z + 2) -16(z + 2)" note -16 as the common factor" z2(z+2)−16(z+2) note -16 as the common factor
=(z+2)(z^2 - 16)(z+2)(z2−16)

=(z + 2)(z + 4)(z - 4)(z+2)(z+4)(z−4)

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