Question

find the roots of the factored polynomial,
$(x + 1)^3(x + 9)$
write your answer as a list of values separated by commas.
$x = $

Explanation:

Step1: Set each factor to zero

To find the roots of a factored polynomial, we set each factor equal to zero and solve for \( x \). For the factor \( (x + 1)^3 \), we set \( x + 1 = 0 \). For the factor \( (x + 9) \), we set \( x + 9 = 0 \).

Step2: Solve for \( x \) from each factor

• For \( x + 1 = 0 \), subtracting 1 from both sides gives \( x = -1 \). Since the factor \( (x + 1) \) is cubed, \( x = -1 \) is a root (with multiplicity 3, but we still list it as a root).
• For \( x + 9 = 0 \), subtracting 9 from both sides gives \( x = -9 \).

Answer:

-1, -9