# What is the residue of (2x^4+7x^3-3x^2-5x-9)÷(x+3)?

Jul 27, 2018

The remainder is $= - 48$

#### Explanation:

Apply the remainder theorem

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

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

Let $x = c$

Then,

$f \left(c\right) = 0 + r$

Here,

$f \left(x\right) = 2 {x}^{4} + 7 {x}^{3} - 3 {x}^{2} - 5 x - 9$

Therefore,

$f \left(- 3\right) = 2 \cdot {3}^{4} - 7 \cdot {3}^{3} - 3 \cdot {3}^{2} + 5 \cdot 3 - 9$

$= 162 - 189 - 27 + 15 - 9$

$= - 48$

The remainder is $= - 48$