Question

How do you use the factor theorem to determine whether x-2 is a factor of `P(x)=2x^3 -7x^2 + 7x - 2`?

Answer 1

Since `P(2)=0`
`color(white)("XXX")(x-2)` is a factor of `P(x)`

Explanation:

The Factor Theorem tells us that
`color(white)("XXX")(x-a)` is a factor of `P(x)` if and only if `P(a)=0`

Given
`color(white)("XXX")P(x)=2x^3-7x^2+7x-2`

then
`color(white)("XXX")P(2)= 2(2^3)-7(2^2)+7(2)-2`

`color(white)("XXX")=2(8)-7(4)+7(2)-2`

`color(white)("XXX")=16-28+14-2`

`color(white)("XXX")=0`

So `(x-2)` is a factor of `P(x)=2x^3-7x^2+7x-2`