How Do You Figure Out a Template for Factoring a Trinomial?

A trinomial is a polynomial with three terms
A binomial is a polynomial with two terms
If the first and last signs of the trinomial are both positive, then the signs of the binomials are both positive
If the last sign of the trinomial is positive and the first sign is negative, then the signs of the binomials are both negative
If the last sign of the trinomial is negative, then one binomial will have a positive sign and one will have a negative sign

1. To figure out the signs of the binomials, we need to look at the signs of the trinomial
2. A trinomial is a polynomial with three terms
3. A binomial is a polynomial with two terms
1. A trinomial is a polynomial with three terms
1. A trinomial is a polynomial with three terms
2. The trinomial here is Ax²+Bx+C
1. We'll look at the last sign of the trinomial to determine the signs of the binomials
1. Here we have two POSITIVE signs
1. A trinomial with two positive signs factors into two binomials, both with positive signs
1. Here our LAST sign is POSITIVE and our FIRST sign is NEGATIVE
1. A trinomial with a positive sign last and a negative sign first factors into two binomials, both with negative signs
1. Here our last sign is NEGATIVE
2. Notice how the first sign has a plus or minus sign
3. This is because it doesn't matter what the sign is - it can be either one
1. One binomial will have a plus sign and one will have a minus sign
1. If the last sign of the trinomial is POSITIVE and the first sign is NEGATIVE, the binomials will both have PLUS signs
2. If the last sign of the trinomial is POSITIVE and the first sign is NEGATIVE, the binomials will both have MINUS signs
3. If the last sign of the trinomial is NEGATIVE, it doesn't matter what the first sign is
4. One binomial will have a PLUS sign and the other will have a MINUS sign

How do you determine the signs of your binomials when factoring a trinomial?