How do you factor #x^3 +5x^2-9x-45#?

1 Answer
Oct 9, 2015

Answer:

#(x+3)(x-3)(x+5)#

Explanation:

Note that #(-9x-45)= (-9)color(blue)((x+5))#
and that #(x^3+5x^2) = (x^2)color(blue)((x+5))#

We can write
#x^3+5x^2-9x-45#
#color(white)("XXX")=(x^2-9)color(blue)((x+5))#

If we further note that #(x^2-9)# is the difference of squares #color(green)((x+3))color(brown)((x-3))#
we can expand this to
#x^3+5x-9x-45#
#color(white)("XXX")=color(green)((x+3))color(brown)((x-3))color(blue)((x+5))#