If polynomial P(x) = x3 - 3x2 + 5x-3 is divided by polynomial G (x) = x2 - 2, the quotient and remainder are:
Dividend = Divisor × quotient + remainder x3 - 3x2 + 5x - 3 = (x2 - 2) × (x - 3) + (7x - 9) x3 - 3x2 + 5x - 3 = (x3 - 3x2 - 2x + 6) + (7x - 9) x3 - 3x2 + 5x - 3 = x3 - 3x2 + 5x - 3 LHS = RHS Hence by using the long division method, the quotient and remainder of the polynomial p(x) = x3 - 3x2 + 5x - 3 when divided by the polynomial g(x) = x2 - 2 are x - 3 and 7x - 9 respectively.
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