Question

on dividing 6xcube+3x square-3x+8 by the polynomial g (x) the quotient and remainder are 3x+4 and -6x+20 Find g (x)

Answer 1

Let the dividend be f(x) = 6x3+3x2-3x+8 Divisor = g(x) quotient = 3x + 4 Remainder = -6x + 20 Recall that dividend = divisor × quotient + Remainder 6x3+3x2-3x+8 = g(x) × (3x +4) + (-6x +20) g(x) × (3x +4) = 6x3+3x2–9x – 12 g(x) = (6x3+3x2–9x – 12)/(3x + 4) divide them to get the quotient.