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

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Answer 1 · 2018-07-27T11:35:32

The remainder is $=-48$

Apply the remainder theorem

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

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

Let $x=c$

Then,

$f(c)=0+r$

Here,

$f(x)=2x^4+7x^3-3x^2-5x-9$

Therefore,

$f(-3)=2*3^4-7*3^3-3*3^2+5*3-9$

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

$=-48$

The remainder is $=-48$