How do you factor the trinomial #x^2 + 13x + 42#?

1 Answer
Mar 31, 2018

#(x+6)(x+7)#

Explanation:

When we look at the trinomial, there is no number (coefficient) in front of #x^2#, so we know that it is a simple trinomial. All you have to do in a simple trinomial is to find two numbers that not only add up to the #b# term, but multiply to the #c# term.

In this trinomial, the #b# term is #13#, so you need to find two numbers that add up to #13#. That could be

  • #5 and 8#
  • #6 and 7#
  • #11 and 2#

and so on. But these two numbers need to multiply to get the #c# term. In this case, it's #42#. So what two numbers add up to #13# and multiply to #42#? The answer is #6# and #7#.

#6+7=13 and 6xx7=42#

After this, all you need to do is put this in binomial form, so take an #x#, and add your first number

#(x+6)#

Then multiply this by another #x +# the second number

#(x+7)#

And there you have the answer:

#(x+6)(x+7)#

If you're ever unsure of your answer, try to expand and simplify the answer. If you go back and the expanded/simplified version is the same trinomial you started with, that means you did it right.