Is the binomial a factor of the polynomial function?

Notice that  f(x)  factors like this...

 

f(x)   =   x³ + 4x² - 9x - 36

                                              Factor  x²  out of the first two terms; factor  -9  out of the last two terms.

f(x)   =   x²(x + 4) - 9(x + 4)

                                              Factor  (x + 4)  out of both remaining terms.

f(x)   =   (x + 4)(x² - 9)

                                              Factor  x² - 9  as a difference of cubes.  x² - 9   =   (x + 3)(x - 3)

f(x)   =   (x + 4)(x + 3)(x - 3)

 

So the factors of  f(x)  are  (x + 4) ,  (x + 3) ,  and  (x - 3) .