Q4 of 44 Page 70

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

Dividend = x3 – 3x2 + x + 2

Quotient = x – 2


Remainder = -2x + 4


Dividend = Divisor × Quotient + Remainder


⇒ x3 – 3x2 + x + 2 = Divisor ×(x – 2) + (-2x + 4)


⇒ x3 – 3x2 + x + 2 – (-2x + 4) = Divisor ×(x – 2)


⇒ x3 – 3x2 + x + 2 + 2x – 4 = Divisor ×(x – 2)


⇒ x3 – 3x2 + 3x – 2 = Divisor ×(x – 2)



Therefore, g(x) = x2 – x + 1


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