Question

on dividing polynomial 3 X square + 4 x square + 5 x minus 13 by g of x their quotient and remainder are to 3 X + 10 and 16 X -43 respectively find g of x​

Answer 1

Given : $3x^3+4x^2+5x-13=g(x)(3x+10)+16x-43$

1. Move the remainder to the left hand side.

$3x^3+4x^2+(5-16)x-13+43=g(x)(3x+10)$

$3x^3+4x^2-11x+30=g(x)(3x+10)$

2. Factor $3x^3+4x^2-11x+30$.

$3x^3+4x^2-11x+30=(3x+10)(x^2-2x+3)$

Thus, $g(x)(3x+10)=(3x+10)(x^2-2x+3)$.

Divide by $3x+10$, and we get $g(x)=x^2-2x+3$.

∴$g(x)=x^2-2x+3$

Answer 2

Step-by-step explanation:

hope it helps....................