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

Sep 26, 2016

$f \left(1\right) = 0$
$\left(x - 1\right)$ is a factor

#### Explanation:

Call the given expression $f \left(x\right)$

$f \left(x\right) = {x}^{3} + 5 {x}^{2} + 2 x - 8$

Let $x - 1 = 0 \text{ "rarr x = 1" }$ subs 1 for x in the expression

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

$f \left(1\right) = {\left(1\right)}^{3} + 5 {\left(1\right)}^{2} + 2 \left(1\right) - 8$

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

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