Question

select the correct answer.
which expression is a factor of this polynomial?
$x^3 + 2x^2 - 9x - 18$
a. $(x - 2)$
b. $(x - 6)$
c. $(x + 2)$
d. $(x + 1)$

Explanation:

Step1: Group polynomial terms

Group first two and last two terms:
$(x^3 + 2x^2) + (-9x - 18)$

Step2: Factor out common terms

Factor $x^2$ from first group, $-9$ from second:
$x^2(x + 2) - 9(x + 2)$

Step3: Factor out shared binomial

Factor $(x+2)$ from both terms:
$(x + 2)(x^2 - 9)$

Step4: Factor difference of squares

Rewrite $x^2-9$ as $(x-3)(x+3)$:
$(x + 2)(x - 3)(x + 3)$

Answer:

C. $(x + 2)$