1. Objective The student will be able to:
factor quadratic trinomials.

2. Terms to remember: Factor Trinomial Quadratic trinomial (y+2)(y+4)
Box/Area method: (y+2)(y+4)

3. 1) Factor. y2 + 6y + 8
How do we decide which factors to use?

4. Let’s practice that next!
1) Factor. y2 + 6y + 8
(y + 2)(y + 4)
When the last term is positive, the factors will have the same sign as the middle term.
When the last term is negative, the factors will have different signs.
Do it! Factor: y2 - 6y + 8
Let’s practice that next!

5. 2) Factor. x2 - 2x - 15 Change the signs of the factors!
+ 3
+3x
- 5
-5x
Write your solution.
(x + 3)(x - 5)

6. Another approach: Use a table of factors and their sums:
Factor y2 + 3y – 18
Factors of -18:
Sum of Factors
-1 and +18
+1 and -18
-2 and + 9
+2 and - 9
-3 and +6
+3 and -6

7. Another approach: Use a table of factors and their sums:
Factor y2 + 3y – 18
Factors:
Sum of Factors
-1 and +18
+17
+1 and -18
-17
-2 and + 9 +7
+2 and - 9 -7
-3 and +6 +3
+3 and -6 -3
Remember we are looking for the combination that results in a middle term of +3y. This means we need the sum of our factors to be +3.

8. Some final advice:
Always remember to arrange your polynomial in standard form before beginning to factor.
Ex. Factor 6x – 7 + x2
Also, always check first for a possible GCF before beginning to factor.
Ex: Factor 2x2y+12xy-14y

9. Use the table of factors and their sums to match the list of trinomials to factored form:
Sum of Factors
Trinomial
Sol.
-1 and +18
+17
(y-1)(y+18)
+1 and -18
-17
(y+1)(y-18)
-2 and + 9 +7
(y-2)(y+9)
+2 and - 9 -7
(y+2)(y-9)
-3 and +6 +3
(y-3)(y+6) A
+3 and -6 -3
(y+3)(y-6)
A. y2+3y-18 B. y2-3y-18 C. y2-17y-18 D. y2+7y -18 E. y2+17y-18 F. y2-7y -18

10. Use the table of factors and their sums to match the list of trinomials to their factored form:
Sum of Factors
Trinomial
Sol.
-1 and +18
+17
(y-1)(y+18) E
+1 and -18
-17
(y+1)(y-18) C
-2 and + 9 +7
(y-2)(y+9) D
+2 and - 9 -7
(y+2)(y-9) F
-3 and +6 +3
(y-3)(y+6) A
+3 and -6 -3
(y+3)(y-6) B
A. y2+3y-18 B. y2-3y-18 C. y2-17y-18 D. y2+7y -18 E. y2+17y-18 F. y2-7y -18

11. In class practice:
Factor:
a2 +12a + 27
14x + x2 + 45
y4 + 5y3 - 84y2
2n2 - 20n + 50
Challenge: use the results from (a) to solve a2 +12a + 27 = 0.