Question

Is x-1 a factor of `x^3+5x^2+2x-8`?

Answer 1

`f(1) = 0`
`(x-1)` is a factor

Explanation:

Call the given expression `f(x)`

`f(x) =x^3+5x^2+2x-8`

Let `x-1=0 " "rarr x = 1" "` subs 1 for x in the expression

In doing this we are finding the remainder without actually having to divide.

`f(1) = (1)^3+5(1)^2+2(1)-8`

`= 1+5+2-8 = 0`

The fact that the answer is `0`, tells us that the remainder is 0.
Actually, there is no remainder.

(x-1) is a factor of the expression