How do you factor the trinomial #a^3 - 6a^2 - 27a#?

1 Answer
Nov 29, 2015

#a(a+3)(a-9)#

Explanation:

To factor any sort of polynomial, you want to look for any common factors. This could be a common factor of a variable or a constant in every term.

In the polynomial #a^3-6a^2-27a#, you can easily recognize the common #a# in every term. To factor out the #a#, divide every term by the #a#.
Doing so gives you:
#a(a^2-6a-27)#

Now, all you have to worry about is the #a^2-6a-27#. Looking at factors of #-27# that add up to #-6#, hopefully you can recognize #3# and #-9#.

Now you have all your factors:

#a(a^2-6a-27) = a(a+3)(a-9)#
or
#a^3-6a^2-27a = a(a+3)(a-9)#