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#