Question

Divide 6x 3 + 13x 2 +x-2 by 2x+1 and find quotient and remainder.

Answer 1

p(x)=6x³+13x²+x-2                 g(x)=2x+1

p(x)=g(x)×q(x)+r(x)
6x³+13x²+x-2=2x+1×q(x)+r(x)
6x³+13x²+x-2/2x+1=q(x)   + r(x)

3x²+5x-2=q(x)[quotient]
6x³+13x²+x-2=2x+1×3x²+5x-2+r(x)

6x³+13x²+x-2=6x³+13x²+x-2+r(x)
6x³+13x²+x-2-(6x³+13x²+x-2)=r(x)
6x³+13x²+x-2-+6x³-13x²-x+2=r(x)

0=r(x)[remainder]