How do you factor completely $P (v) = v^{3} + v^{2} - 16 v - 16$ $P(v)=v^3+v^2-16v-16$ ?

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Answer 1 · 2017-01-09T18:40:09

The answer is $= (v + 1) (v - 4) (v + 4)$ $=color(red)((v+1))color(blue)((v-4)(v+4))$

We use

$a^{2} - b^{2} = (a + b) (a - b)$ $a^2-b^2=(a+b)(a-b)$

$P (v) = v^{3} + v^{2} - 16 v - 16$ $P(v)=v^3+v^2-16v-16$

$= v^{2} (v + 1) - 16 (v + 1)$ $=v^2color(red)((v+1))-16color(red)((v+1))$

$= (v + 1) (v^{2} - 16)$ $=color(red)((v+1))color(blue)((v^2-16))$

$= (v + 1) (v - 4) (v + 4)$ $=color(red)((v+1))color(blue)((v-4)(v+4))$

How do you factor completely P(v)=v3+v2−16v−16P(v)=v^3+v^2-16v-16?