Question

select the correct answer.

which expression is a factor of this polynomial?

\\x^3 + 2x^2 - 9x - 18\\

\\((x - 6)\\)
\\((x + 1)\\)
\\((x - 2)\\)
\\((x + 2)\\)

Explanation:

Group the terms of the polynomial

$$ (x^3 + 2x^2) - (9x + 18) $$

Factor out the greatest common factor from each group

$$ x^2(x + 2) - 9(x + 2) $$

Factor out the common binomial factor and simplify

$$ (x^2 - 9)(x + 2) = (x - 3)(x + 3)(x + 2) $$

Answer:

• (x - 6)
• (x + 1)
• (x - 2)
• (x + 2) (Correct answer)