# How do you use the remainder theorem to find the remainder of (x^3 - 5x^2 + 7x +3) ÷ (x-2)?

Mar 21, 2018

Put 2 as the value of $x$ in the dividend

#### Explanation:

The remainder theorem states that every polynomial,
For Ex - p( $x$ )= ${x}^{2} + x + 1$
if divided by a polynomial of the form - ( $x - a$ )
will give remainder as p($a$) = (In this case) ${a}^{2} + a + 1$

Here:
p($x$) = $\left({x}^{3} - 5 {x}^{2} + 7 x + 3\right)$
g($x$) = $\left(x - 2\right)$

So,
p($2$) = $\left({2}^{3} - 5 \cdot {2}^{2} + 7 \cdot 2 + 3\right)$
= $\left(8 - 20 + 24 + 3\right)$
= $15$
Remainder = 15