Question

How do you use the factor theorem to determine whether x-3 is a factor of `p(x)=x^3-4x^2+3x`?

Answer 1

The Factor Theorem says that
`(x-a)` is a factor of `p(x)` if and only if `p(a)=0`

In this case, since `p(3)=0`
`color(white)("XXX") (x-3)` is a factor of `p(x)=x^3-4x^2+3x`

Explanation:

`p(3)= 3^3-4*3^2+3*3 = 27-36+9 = 0`