Is the binomial a factor of the polynomial function? f (x) = x3+2x2-16x-32

Select Yes or No for each binomial.

(x-2)

(x+2)

(x-4)

(x+4)

(x+6)

Since it is x^3 cubed it has 3 maximum roots

by the zero multiplication property of function

if you plug find a root then you can deduce it is a factor in other words if f (x) = (x-a) (x-b)

then f (a) = 0 and f (b) = 0

so

f (2) = 8+8-32-32 = - 48 therefore it is not a factor

f (-2) = - 8+8+32-32=0 hence it is a factor

f (4) = 64+32-64-32=0 it is a factor

f (-4) = - 64+32+64-32=0 it is a factor

f (-6) it is not a factor via the fundmental therom of algebra

f (x) = (x+2) (x-4) (x+4)

= (x^2-16) (x+2) = x^3+2x^2-16x-32 which checks our work