Question

which of the binomials below is a factor of this trinomials x2+5x+6

Answer 1

x^2 + 5x + 6

Do you know how to F.O.I.L. binomials?
(First, outside, inside, last)

The problem above is like "reverse foil".
You have to find what the numbers and variables have in common...

The first number (x^2) has 2 x's which you can only get by multiplying 2 x's together:

(x + ?) (x + ?)

To get the last number (6) you need to find 2 numbers that equal six when multiplied:
This could be 1 and 6, or 2 and 3

But to pick which one, you have to look at the middle number (5x).

When you FOIL, and do O and I (outside and inside) you will get two different numbers that you will combine, because they will be "like-terms".

So you have to work those possibilities out:

(x+1) (x+6) = x^2 + 6x + 1x + 6
= x^2 + 7x + 6 .... So this one isn't it.

However,
(x+2) (x+3) = x^2 + 3x + 2x + 6
= x^2 + 5x + 6

So you would use the second binomial!
:)