Question

On dividing x^3+x^2+x-2 by polynomial g(x), the quotient and remainder were x^2+2x+1 and 2 x-1 respectively, find g(x)

Answer 1

Answer:

g(x) = (x-1)

Step-by-step explanation:

let p(x) = x³+x²+x-2

    q(x) = x²+2x+1

    r(x) = 2x-1

given p(x) / g(x) gives quotient q(x) and remainder r(x)

d⇒ p(x) = q(x)*g(x) + r(x)

  ⇒ g(x) =  [ p(x)-r(x) ] / q(x) ]

             = (x³+x²+x-2  -(2x-1))  ÷  ( x²+2x+1)

             = ( x³+x²+x-2- 2x+1) ÷ (x+1)²

             = (x³+x²-x-1)÷ (x+1)²

             = (x²(x+1) - (x+1)) ÷ (x+1)²

            = (x+1)(x²-1)÷ (x+1)²

            = (x+1)(x+1)(x-1)÷ (x+1)²

     g(x) = (x-1)