How do you use the remainder theorem to determine the remainder when the polynomial #(x^3+2x^2-3x+5) div(x-3)#?

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Answer 1 · 2017-03-03T12:48:17

The remainder is #=41#

When we divide the polynomial #f(x)# by #(x-c)#

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

and

#f(c)=0+r=r#

Here,

#f(x)=x^3+2x^2-3x+5#

and

#c=3#

So,

#f(3)=3^3+2*3^2-3*3+5#

#=27+18-9+5#

#=41#