Q17 of 25 Page 2

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).

Given:
Polynomial, p(x) = x3 – 3x2 + x + 2 (dividend)


Quotient = (x − 2)


Remainder = (− 2x + 4)


To find: divisor = g(x)


Explanation:
we know,
Dividend = Divisor × Quotient + Remainder
⇒ x3 – 3x2 + x +2 = g(x) × (x – 2) + (–2x + 4)


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


⇒ x3 – 3x2 + 3x – 2 = g(x)(x – 2)


g(x) is the quotient when we divide (x3 – 3x2 + 3x – 2) by (x – 2)



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