How do you factor $z^{3} + 2 z^{2} - 16 z - 32$ $z^3 + 2z^2 - 16z - 32$ by grouping?

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How do you factor $z^{3} + 2 z^{2} - 16 z - 32$ $z^3 + 2z^2 - 16z - 32$ by grouping?

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Answer 1 · 2016-06-13T20:11:54

$(z + 2) (z + 4) (z - 4)$ $(z + 2)(z + 4)(z - 4)$

Explanation:

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

$(z^{3} + 2 z^{2}) + (- 16 z - 32) common factor from each pair$ $(z^3 + 2z^2) + (-16z -32) " common factor from each pair"$
= $z^{2} (z + 2) - 16 (z + 2) note -16 as the common factor$ $z^2(z + 2) -16(z + 2)" note -16 as the common factor"$
= $(z + 2) (z^{2} - 16)$ $(z+2)(z^2 - 16)$

= $(z + 2) (z + 4) (z - 4)$ $(z + 2)(z + 4)(z - 4)$

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How do you factor $z^{3} + 2 z^{2} - 16 z - 32$ $z^3 + 2z^2 - 16z - 32$ by grouping?

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