Question

On dividing x3-3x2+x+2 by a polynomial g(x) the quotient and the remainder were found to be x-2 and -2x+4 respectively. Find g(x)

Answer 1

As We know that the Polynomial f(x) = x³–3x²+x+2.

• Dividend p(x) = x³–3x²+x+2
• Quotient = x–2
• Remainder = –2x+4

As we also know that,

» {Dividend = Divisor × Quotient + Remainder}

→ x³-3x²+x+2 = g(x)×(x-2) + (-2x+4)

→ x³-3x²+x+2-(-2x+4) = g(x)×(x-2)

→ g(x) × (x-2) = x³-3x²+3x-2

Finally, for finding g(x) we have to divide x³-3x²+3x-2 with (x-2).

After dividing, we got that g(x) = (x²–x+1).