Question

find the roots of the factored polynomial,
$(x - 4)^3$
write your answer as a list of values separated by commas,
x =

Explanation:

Step1: Set the polynomial to zero

To find the roots of the polynomial \((x - 4)^3\), we start by setting the polynomial equal to zero: \((x - 4)^3=0\).

Step2: Solve for x

Taking the cube - root of both sides of the equation \((x - 4)^3 = 0\), we know that if \(y^3=0\), then \(y = 0\). Here, \(y=x - 4\), so \(x-4 = 0\). Solving for \(x\) by adding 4 to both sides of the equation, we get \(x=4\). Since the factor \((x - 4)\) is cubed, the root \(x = 4\) has a multiplicity of 3, but we still list it as a single value in the list of roots (because we are just asked for the values of the roots, and a repeated root is still the same value).

Answer:

4