Question

when g(x) is divided by x^2+x-6 the remainder is 7x+13 . what is the remainder when g(x) is divided by x+3

Answer 1

Answer: (x - 2)(7x + 13) which is equivalent to 7x² - x - 26

Explanation:

`.\qquad (g(x))/(x^2+x-6)=7x+13\\\\\\\implies g(x)=(x^2+x-6)(7x+13)\\\\.\qquad \qquad =(x+3)(x-2)(7x+13)\\\\\\\text{What is g(x) divided by x+3?}\\\\(g(x))/(3)=((x+3)(x-2)(7x+13))/(x+3)\\\\\\.\qquad =(x-2)(7x+13)\\\\\\.\qquad =7x^2+13x-14x-26\\\\\\.\qquad =\large \boxed{7x^2-x-26}`