Question

On dividing the polynomial 3x3+4x2+5x-13 by the polynomial g(x) , the quotient and the remainder were (3x+10) and (16x-43) respectively. Find g(x)

Answer 1

Dividend= Divisor X quotient + Remainder
$3 {x}^{3} + 4 {x}^{2} + 5x - 13 = \\ g(x)(3x + 10) + (16x - 43) \\ 3 {x}^{3} + 4 {x}^{2} + 5x - 16x - 13 + 43 = \\ g(x)(3x + 10) \\ 3 {x}^{3} + 4 {x}^{2} - 11x + 30 = g(x)(3x + 10) \\ g(x) = \frac{3 {x}^{3} + 4 {x}^{2} - 11x + 30 }{3x + 10} \\ g(x) = {x}^{2} - 2x + 3$
is the answer