If (x^2-5x-6)/(x^3+ax^2+bx+c simplifies to 1/(x+2), then a + b + c = ?

1 Answer
Nov 9, 2017

-21.

Explanation:

Given that, (x^2-5x-6)/(x^3+ax^2+bx+c)=1/(x+2).

By Cross Multiplication, we get,

x^3+ax^2+bx+c=(x^2-5x-6)(x+2), i.e.,

=(x-6)(x+1)(x+2),

=x(x^2-5x-6)+2(x^2-5x-6),

=(x^3-5x^2-6x)+(2x^2-10x-12).

rArr x^3+ax^2+bx+c=x^3-3x^2-16x-12.

Comparing the co-efficients of polynomials on both sides, we have

a=-3, b=-16, and, c=-12.

:. a+b+c=-21, as desired.

Enjoy Maths.!