on dividing the polynomial 4x4 - 5x3 - 39x2 - 46x

Question

On dividing the polynomial 4x⁴ - 5x³ - 39x² - 46x - 2 by the polynomial g(x) the quotient is x² - 3x - 5 and the remainder is -5x + 8.Find the polynomial g(x). (Ans:4 x²+7x+2)

Ans:    p(x) = g (x) q (x) + r (x)

g(x) =p( x) - r( x)/q( x)

let p(x) = 4x⁴ - 5x³ - 39x² - 46x - 2 q(x) = x² - 3x - 5 and r (x) = -5x + 8

now p(x) - r(x) = 4x⁴ - 5x³ - 39x² - 41x - 10

when p( x) - r( x)/q( x)

∴ g(x) = 4x² + 7x + 2

= 4x² + 7x +2