Question

select the correct answer.
which expression is a factor of this polynomial?
x³ + 2x² - 9x - 18
a. (x - 2)
b. (x + 1)
c. (x + 2)
d. (x - 6)

Explanation:

Step1: Factor by grouping

Group the terms: $(x^3 + 2x^2) + (-9x - 18)$
Factor out common terms: $x^2(x + 2) - 9(x + 2)$

Step2: Factor out the common binomial

Now, factor out $(x + 2)$: $(x + 2)(x^2 - 9)$

Step3: Factor the difference of squares

Notice that $x^2 - 9$ is a difference of squares, so $x^2 - 9 = (x - 3)(x + 3)$
So the factored form is $(x + 2)(x - 3)(x + 3)$

Answer:

C. $(x + 2)$