Find the equation for the end-behavior asymptote (horizontal/slant,etc) of f(x)= (4x^3-17x^2+15x-7)/(x^2+5x+6) write the asymptote as y=

Question

having trouble on how to come up with an equation for the end behavior asymptote. I know you are supposed to factor down the denominator which is (x+2)(x+3) but I am at a loss after that 

Answer 1

Divide the numerator by denominator using long division.

 

                                           4x - 37

                     ___________________

(x² + 5x + 6) | 4x³ - 17x² + 15x - 7

                      4x³ + 20x² + 24x

                     ___________________

                            -37x²   -  9x  - 7

                            -37x² - 185x - 222

                           _________________

                                      176x  + 215

 

 

The quotient is your slant asymptote.

 

Slant asymptote is   y = 4x - 37