Verified answer

According to the division algorithm,

Dividend = Divisor × Quotient + Remainder

We have,

Dividend = x3 - 3x2 + x + 2, Divisor = g(x), Quotient = x - 2 and Remainder = -2x + 4

Put the given values in the below equation and simplify it, to get the value of g (x).

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 + x + 2x + 2 - 4) = g (x) × (x - 2)

(x3 - 3x2 + 3x - 2) = g (x) × (x – 2)

g (x) = (x3 - 3x2 + 3x - 2) / (x – 2)

Therefore, g (x) = x2 - x + 1

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divide the polynomial : x³-3x²-x+3 by x²-2x-3 also find the quotient and the remainder