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Divide 5x3-13r + 2 1x-14 by (3-2x + x") and verify the division algorithm. |
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Answer» Given f(x) = 5x^3 - 13x^2 + 21x - 14. Given g(x) = 3 - 2x + x^2. We need to divide f(x) by g(x). 5x - 3 ---------------------------------= > x^2 - 2x + 3) 5x^3 - 13x^2 + 21x - 14 5x^3 - 10x^2 + 15x --------------------------------- -3x^2 + 6x - 14 - 3x^2 + 6x - 9 ----------------------------------- -5. Here, Dividend = 5x^3 - 13x^2 + 21x - 14 Divisor = 3 - 2x + x^2 Quotient = 5x - 3 Remainder = -5 Division Algorithm: Dividend = Divisor * Quotient + Remainder = (3 - 2x + x^2) * (5x - 3) + (-5) = 15x - 9 - 10x^2 + 6x + 5x^3 - 3x^2 - 5 = 5x^3 - 13x^2 + 21x - 14. LHS = RHS |
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