# How do you find the remainder when f(x)=5x^6-3x^3+8; x+1?

May 7, 2016

The remainder theorem states that whenever polynomial function $f \left(x\right)$ is divided by $x - a$ the remainder is given by evaluating $f \left(a\right)$

#### Explanation:

$x + 1 = 0$
$x = - 1$

You will evaluate $f \left(- 1\right)$

$f \left(- 1\right) = 5 {\left(- 1\right)}^{6} - 3 {\left(- 1\right)}^{3} + 8$

$f \left(- 1\right) = 5 \left(1\right) - 3 \left(- 1\right) + 8$

$f \left(- 1\right) = 5 + 3 + 8$

$f \left(- 1\right) = 16$

Hence, the remainder will be 16.

Hopefully this helps!