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#