Question

divide x^19+x^17+x^13+x^11+x^7x^5+x^3 by x^2+1 and verify​

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Divide 5x^3-13x^2+21x-14 by 3-2x+x^2 and verify the division algorithm.

Answer · 116 votes

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 - 14Divisor = 3 - 2x + x^2Quotient = 5x - 3Remainder = -5Division 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 = RHSHope this helps!

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