How do you find the remainder for #(x^3+11x^2+24x+9)div(x+2)#?

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Answer 1 · 2016-09-13T04:18:00

#" The Remainder"=-3#.

We will use the Remainder Theorem :

#"A poly. "P(x)," when divided by "(px+q)" leaves remainder "P(-q/p)#.

Let #P(x)=x^3+11x^2+24x+9#.

Comparing #(x+2)# with #(px+q), p=1, q=2#.

Hence by the Remainder Theorem,

The Remainder#=P(-q/p)=P(-2)#

#=(-2)^3+11(-2)^2+24(-2)+9#

#=-8+44-48+9#.

#:." The Remainder"=-3#.

Enjoy Maths.!