Question

find the roots of the factored polynomial.
$(x - 1)^3(x - 6)$
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 \((x - 1)^3(x - 6)\), we set each factor equal to zero. For the factor \((x - 1)^3\), we have \(x - 1 = 0\). For the factor \((x - 6)\), we have \(x - 6 = 0\).

Step2: Solve for x

Solving \(x - 1 = 0\) gives \(x = 1\). Solving \(x - 6 = 0\) gives \(x = 6\). Even though \((x - 1)\) is cubed, the root \(x = 1\) is still just \(1\) (the multiplicity affects the graph but not the root value itself here).

Answer:

1, 6