The polynomial p(x)=x^3-6x^2+32p(x)=x 3 −6x 2 +32p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 6, x, squared, plus, 32 has a known factor of (x-4)(x−4)left parenthesis, x, minus, 4, right parenthesis.

Step-by-step explanation:

Given the polynomial function p(x)=x^3-6x^2+32, if x-4 is a factor, then we can find the remainder if the polynomial is divided by x -4.

First we need to equate the function x - 4 to zero and find x;

x - 4 = 0

x= 0+4

x = 4

Next is to substitute x = 4 into the expression p(x)=x^3-6x^2+32

p(x)=x^3-6x^2+32

p(4)=(4)^3-6(4)^2+32

p(4) = 64 - 96 + 32

p(4) = 0

Hence the remainder when x-4 is divided by the polynomial is zero