How do you factor completely #x^2+2x+3x+6#?

1 Answer
Dec 16, 2015

Answer:

Factor by grouping to find:

#x^2+2x+3x+6=(x+3)(x+2)#

Explanation:

Factor by grouping as follows:

#x^2+2x+3x+6#

#=(x^2+2x)+(3x+6)#

#=x(x+2)+3(x+2)#

#=(x+3)(x+2)#

With this question, the hard/fun part has already been done for you, viz splitting the #x# term into #2x+3x#. Normally you would be given something like #x^2+5x+6# and have to find the split yourself.

If you did have to find the split yourself, you would look for two numbers which add up to #5# and multiply together to give #6#.

Notice that in general, #(x+a)(x+b) = x^2+(a+b)x+ab#