Question

if a polynomial x^3+4x^2-7x+8 by g(x), then quotient and remainders are (x+2),-10x+10, respectively,then find g(x)​

Answer 1

Answer:

as we the division algorithm on page no.34 of ncert maths book of class 10 that is :

p(x)=g(x) ×q(x)+r(x)

so,

x^3+4x^2-7x+8=g(x)×(x+2)-(10x-10)

x^3+4x^2-7x+8+(10x-10)=g(x)×(x+2)

x^3+4x^2-7x+8+10x-10=g(x)×(x+2)

x^3+4x^2+3x-2=g(x)×(x+2)

x^3+4x^2+3x-2/x+2=g(x)

on dividing x+2 with x^3+4x^2+3x-2 we will get x^2+2x-1

so ,

g(x) = x^2+2x-1