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Question
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)
Solution
p(x) = x3-3x2+x+2 (Dividend)
g(x) = ? (Divisor)
Quotient = (x - 2)
Remainder = (-2x + 4)
Dividend = Divisor × Quotient + Remainder
x3 - 3x2 + x + 2 = g(x) 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)
∴ g(x) = (x^2 - x + 1)
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