Question

find the roots of the factored polynomial.
(x - 6)(x + 4)(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 a factored polynomial, we set each factor equal to zero. For the factor \(x - 6\), we have \(x - 6 = 0\). For the factor \(x + 4\), we rewrite it as \(x - (-4)=0\), so \(x + 4 = 0\) is equivalent to \(x=-4\). For the factor \(x + 2\), we rewrite it as \(x - (-2)=0\), so \(x + 2 = 0\) is equivalent to \(x=-2\).

Step2: Solve for x in each equation

• For \(x - 6 = 0\), adding 6 to both sides gives \(x = 6\).
• For \(x + 4 = 0\), subtracting 4 from both sides gives \(x=-4\).
• For \(x + 2 = 0\), subtracting 2 from both sides gives \(x=-2\).

Answer:

6, -4, -2