Q. 44.4( 324 Votes )

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).

Answer :

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

Quotient = (x − 2)

Remainder = (− 2x + 4)

To find : divisor = g(x)
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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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).