Question

find the roots of the factored polynomial, x(x + 7)(x + 2) write your answer as a list of values separated by commas. x =

Explanation:

Step1: Set each factor to zero

To find the roots of the polynomial \( x(x + 7)(x + 2) \), we set each factor equal to zero because if a product of factors is zero, then at least one of the factors must be zero (Zero - Product Property).

• For the factor \( x \):

Set \( x=0 \). This is one root.

• For the factor \( x + 7 \):

Set \( x+7 = 0 \). Solving for \( x \), we subtract 7 from both sides of the equation: \( x=-7 \).

• For the factor \( x + 2 \):

Set \( x + 2=0 \). Solving for \( x \), we subtract 2 from both sides of the equation: \( x=-2 \).

Answer:

0, -7, -2