x^3+6x^2-7x-60

Question

what is the answer to this equation

Answer 1

Are you looking for the roots of this polynomial?  The factors?

 

By inspection, -4 is a root.  So, x - (-4)  = x + 4 is a factor.

 

Divide synthetically by x + 4:     -4⌋   1      6     -7     -60

                                                                       -4    -8      60

                                                              1       2    -15       0

 

So, x³ + 6x² - 7x - 60 = (x + 4)(x² + 2x - 15)

 

                                      = (x + 4) (x + 5)(x - 3)

 

Setting each factor to zero, the roots are x = -4, -5, 3.