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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