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

1 Answer
Nov 9, 2017

a + b + c = 9

Explanation:

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

It follows that:

(x^2-5x-6)(x-2)=x^3+ax^2+bx+c

Multiply

x(x^2-5x-6) - 2(x^2-5x-6) = x^3+ax^2+bx+c

x^3-5x^2-6x - 2x^2+10x+12 = x^3+ax^2+bx+c

Combine like terms:

x^3-7x^2+4x+12 = x^3+ax^2+bx+c

Match coefficients:

a = -7, b = 4, and c = 12

a + b + c = -7+ 4 + 12

a + b + c = 9