Question

On dividing 3x^3-2x^2+5x+5 by a polynomial p(x), the quotient and

remainder are x2-x+2 and 3 respectively. Find p(x).

Answer 1

Answer:

If we divide f(x)=3x3+x2+2x+5 by g(x) we get q(x)=(3x−5) as quotient and r(x)=(9x+10) as remainder.

By using division algorithm,

f(x)=g(x)q(x)+r(x)

⟹3x3+x2+2x+5=g(x)(3x−5)+(9x+10)

⟹g(x)=(3x−5)3x3+x2+2x+5−9x−10

⟹g(x)=(3x−5)3x3+x2−7x−5

Hence, g(x)=x2+2x+1