How do you find the zeros for f(x)=x^3+x^2-16x-16

Question

I'm not sure exactly how to start this

Answer 1

factor by grouping:  (x^3 + x^2) -(16x +16)

you can take x^2 out of the first 2 and get x^2(x+1)

take 16 out of 2nd 2 and get 16(x+1)

looks like x^2(x+1) - 16(x+1)

if you think of it as "un-distributing" it becomes (x^2-16)(x+1)

x^2-16 then factors into (x+4)(x-4) so it all looks like (x+4)(x-4)(x+1)=0

set each factor equal to zero x+4=0, x-4=0, x+1=0 and solve

x=-4,4,-1

Answer 2

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