# How do you use the remainder theorem to find the remainder for each division (x^2-2)div(x-1)?

Oct 11, 2017

Quotient $\left(x + 1\right)$ & Remainder $3$

#### Explanation:

$$          x          1
………………………………………………………


x-1 | x^2 0 2
| x^2 -x
|__
0 x 2
x -1
_

0 3 (Remainder)

Oct 11, 2017

The remainder is $- 1$. See explanation.

#### Explanation:

The remainder theorem says that:

For a polynomial $P \left(x\right)$ the remainder of division $P \left(x\right) \div \left(x - a\right)$ is equal to $P \left(a\right)$.

So instead of using the long division to calculate the remainder only you can substitute $a$ to $P \left(x\right)$. Here we have:

$a = 1$, $P \left(x\right) = {x}^{2} - 2$, so:

$P \left(1\right) = {1}^{2} - 2 = 1 - 2 = - 1$

The remainder of dividision $\left({x}^{2} - 2\right) \div \left(x - 1\right)$ is $- 1$