1. Factoring Trinomials with Last Term POSITIVE Guess & Check Method

2. Sign Rule:
When the last term is POSITIVE, the middle sign will be SAME inside BOTH sets of parentheses as the middle term

3. How to Factor a Trinomial
Check for GCF 1st. Divide out the GCF of each term if one exists.
When factoring ax2 + bx + c, first find factors of a and c.
Check the products of the inner and outer terms to see if the sum is b.
When c is POSITIVE, both signs inside the parentheses will be the same as the middle term.

4. 1. 2x2 – 5x + 3 1x 2x -1 -3
( – )( – )
x x

5. 2. 5x2 + 11x + 2 1x 5x +1 +2
( )( )
x x

6. 3. 2x2 – 7x + 5 1x 2x -1 -5
( – )( – )
x x

7. 4. 6x2 – 11x + 3 1x 2x 6x 3x -1 -3
( – )( – )
2x x

8. 5. 4x2 + 16x + 15 +1
+15 +3 +5 1x 2x 4x
( )( )
2x x

9. Factoring Trinomials with Last Term NEGATIVE Guess & Check Method

10. Sign Rule:
When the last term is NEGATIVE, the sign inside the parentheses will DIFFERENT.
If b is Positive, then the LARGER number on the loop will need to be positive.
If b is Negative, then the LARGER number on the loop will need to negative.

11. How to Factor a Trinomial
Check for GCF 1st. Divide out the GCF of each term if one exists.
When factoring ax2 + bx + c, first find factors of a and c.
Check the products of the inner & outer terms to see if the sum is b.
When c is NEGATIVE, signs inside the parentheses will be DIFFERENT.

12. 1. 3x2 – 20x – 7 1x 3x 1 7
( )( )
x x –

13. 2. 2x2 + 3x – 5 1x 2x 1 5
( )( )
x x –

14. 3. 5m2 + 14m – 3 1m 5m 1 3
( )( )
m m –

15. 4. 2x2 – 11x – 21 1x 2x 1 3 7 21
( )( )
x x –

16. Class Work
Factoring WS