# How do you use the remainder theorem to find the remainder for the division (2x^4+4x^3-x^2+9)div(x+1)?

Jan 25, 2017

The remainder is $= 6$

#### Explanation:

When we divide a polynomial $f \left(x\right)$ by $\left(x - c\right)$, we get

f(x)=(x-c)q(x))+r(x)

$q \left(x\right)$ is the quotient

$r \left(x\right)$ is the remainder

When $x = c$

$f \left(c\right) = \left(c - c\right) q \left(x\right) + r$

$f \left(c\right) = r$, the remainder

Here we have,

$f \left(x\right) = 2 {x}^{4} + 4 {x}^{3} - {x}^{2} + 9$

and we divide by $\left(x + 1\right)$

Therefore,

$f \left(- 1\right) = 2 - 4 - 1 + 9 = 6$

The remainder is $= 6$