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

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Answer 1 · 2017-01-25T07:00:40

The remainder is $=6$

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

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

$q(x)$ is the quotient

$r(x)$ is the remainder

When $x=c$

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

$f(c)=r$ , the remainder

Here we have,

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

and we divide by $(x+1)$

Therefore,

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

The remainder is $=6$

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