Question

on dividing x^3-5x^2+6x-4 by a polynomial g(x), the quotient and the remainder were (x-3) and (-4) respectively. find g(x)​

Answer 1

Your answer is given below ---

Using Division algorithm,

p(x) = q(x) × g(x) + r(x)

Then,

x³-5x²+6x+4 = (x-3) × g(x) + 4

x³-5x²+6x+4-4 = (x-3) × g(x)

g(x) = (x³-5x²+6x) / (x-3)

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On, Dividing g(x) = x²-2x

Hence g(x) = x²-2x (or) x²-2x+0