How do you factor #x^2+9x+18#?

1 Answer
Apr 21, 2018

Answer:

By finding what multiplies to give 18 and adds to give 9.

Explanation:

General form #ax^2+bx+c#
What does multiplies to give #ac# and adds to give #b#

First is 18 positive or negative. If positive both factors will be positive or negative depending on the sign of #b#.
(Not this Question) If negative the factors will be opposite in sign.

List all the factors of #ac = 18#.
#1,18#
#2,9#
#3,6#
Now looking at these number intuitively what will add to give #b = 9#.

#3,6#

Now place into the form:
#(x+6)(x+3)#
This is the factorised version of #x^2+9x+18#

Quadratic Equation also works.