What is the remainder when #(x^3 - 2x^2 + 5x - 6) div(x - 3)#?

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Answer 1 · 2018-06-12T06:39:15

The remainder is #=18#

Apply the remainder theorem :

When the polynomial #f(x)# is divided by #(x-c)#, then

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

And when #x=c#

#f(c)=0*q(x)+r=r#

where #r# is the remainder

Here,

#f(x)=x^3-2x^2+5x-6#

and

#c=3#

Therefore,

#f(3)=27-18+15-6=18#

The remainder is #=18#