You might be wondering where the 30 and the 11 come from in the number puzzle.
Well we actually multiply the coefficient of the x squared term and the constant
term together to get this top number. This bottom number 11 comes from our x
term. Whenever we want to factor a trinomial we can set up a number puzzle and
then find the two factors we need to rewrite the x term. So, I can rewrite this
expression as x squared plus 5x plus 6x plus 30. We can rewrite the 11x as 5x
and 6x. The 2 numbers come from our number puzzle. By rewriting this x term as
5x plus 6x we can use factoring by grouping. I remove an x from the first 2
terms and a six from the second two terms. And whoa, look at that, our factored
form. So for any quadratic trinomial, we can try this process to factor it. We
can find two factors of a times c, that sum to the middle number b. We'll
rewrite the middle term using those factors and then try factoring by grouping.