Question

How do you determine whether x-1 is a factor of the polynomial `2x^3+4x^2-5x-1`?

Answer 1

`(x-1)` is a factor of `p(x)`.

Explanation:

Let us denote the poly. by `p(x), so, p(x)=2x^3+4x^2-5x-1.`

A very simple test to check whether `(x-1)` is a factor of `p(x) :` is

`(x-1)" is a factor of "p(x) iff" the sum of the co-effs. of "p(x)" is zero."`

Here, in our Example, the sum of co-effs. of

`p(x)=2+4-5-1=0`

Hence, `(x-1)` is a factor of `p(x)`.