On dividing the polynomial 4x^{4} - 5x^{3} - 39x^{2} - 46x - 2 by the polynomial g(x) the quotient is x^{2} - 3x - 5 and the remainder is -5x + 8.Find the polynomial g(x). (Ans:4 x^{2}+7x+2)
Ans: p(x) = g (x) q (x) + r (x)
g(x) =p( x) - r( x)/q( x)
let p(x) = 4x^{4} - 5x^{3} - 39x^{2} - 46x - 2 q(x) = x^{2} - 3x - 5 and r (x) = -5x + 8
now p(x) - r(x) = 4x^{4} - 5x^{3} - 39x^{2} - 41x - 10
when p( x) - r( x)/q( x)
∴ g(x) = 4x^{2} + 7x + 2
= 4x^{2} + 7x +2