In factoring trinomials, the knowledge of basic factoring comes to play.
For example, the factors of 30 are 6 and 5, -5 and -6, 10 and 3, -10 and -3, 2 and 15, and -2 and -15.
For letters A and B, what we need to consider only here is the constant term, +30 and -54, because our first term x² has 1 as its numerical coefficient only. We need to list down the factors of +30 and -54.
Factors of +30 are:
1. 6 and 5
2. -6 and -5
3. 10 and 3
4. -10 and -3
5. 2 and 15
6. -2 and -15
Out of these 6 factors, which would result in -13 (the second term in the trinomial)?
6 and 5 = 11
-6 and -5 = -11
10 and 3 = 13
-10 and -3 = -13
2 and 15 = 17
-2 and -15 = -17
SInce -10 and -3 would result in -13 when added, the factors of our trinomial in letter A is:
Now, let's factor B.
Let's list down the factors of -54 and add them.
1. -9 and 6 = -3
2. -6 and 9 = 3
We don't need to list down all the factors since we already have here the result "3" in the list of factors. Again, we are looking for the second term to come up and the second term in Letter B is 3x.
Therefore, the factors of the trinomial in Letter B are:
