Answer:
Please check the explanation.
Step-by-step explanation:
Given the polynomial function
[tex]f\left(x\right)\:=x^3+2x^2-16x-32[/tex]
Let us determine the factors by solving
[tex]\:\left0\right\:=x^3+2x^2-16x-32\:[/tex]
[tex]\left(x+2\right)\left(x+4\right)\left(x-4\right)=0[/tex]
Using the zero factor principle:
if [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]x+2=0\quad \mathrm{or}\quad \:x+4=0\quad \mathrm{or}\quad \:x-4=0[/tex]
Thus, (x+2) (x+4) and (x-4) are the factors of the polynomial function.
Therefore,
YES
And (x-2) (x+6) are not the factors of the polynomial function.
Therefore,
YES
