Question

On dividing 2x^3 + 4x^2+ 5x− 13 by a polynomial .g(x)the quotient and the

remainder were 2xand 7 − 5x respectively. Find .g(x)

Answer 1

g(x) = (p(x) - remainder ) / quotient

g(x)=
$(2x {}^{3} + 4x {}^{2} + 10x - 20) \div 2x$

$= {x}^{2} + 2x + 5 - \frac{10}{x}$