Mathematics: Please help me with this math!

hello,, see the attached files.....

Please help me with this math! - id9387680, lamwil9432

peaceouthjkdrb2398

11.02.2022

Please check the explanation.

Step-by-step explanation:

Given the polynomial function

$f\left(x\right)\:=x^3+2x^2-16x-32$

Let us determine the factors by solving

$\:\left0\right\:=x^3+2x^2-16x-32\:$

$\left(x+2\right)\left(x+4\right)\left(x-4\right)=0$

Using the zero factor principle:

if $ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$x+2=0\quad \mathrm{or}\quad \:x+4=0\quad \mathrm{or}\quad \:x-4=0$

Thus, (x+2) (x+4) and (x-4) are the factors of the polynomial function.

Therefore,

YES

(x+2)(x+4)(x-4)

And (x-2) (x+6) are not the factors of the polynomial function.

Therefore,

YES

(x-2)(x+6)

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