1. Warm Up
SUM-PRODUCT PUZZLES
For each figure below, find the pair of numbers whose product is the top number in the X and whose sum is the bottom number in the X. 14 14
-33 2 7 -2 -7 -3 11 9 -9 8 -4 56 6 2 -2 -8 -7 -2 -3
-15 -5

2. Math 8H 8-3 Factoring Trinomials x2 + bx + c
Algebra Glencoe McGraw-Hill JoAnn Evans

3. The Sum-Product Puzzles you did in the warm-up are a useful tool when factoring quadratic trinomials.
Today we’ll factor quadratic trinomials that have a leading coefficient of 1.
They’ll look like this: ax2 + bx + c. The number that replaces the variable “a” will always be 1 in this lesson.

4. Put b in the bottom. It will be the sum of the two side numbers.
ax2 + bx + c
To use this tool, draw an X next to each problem. Multiply a  c and put the product in the top of the figure. This number will be the product of the two side numbers.
Put b in the bottom. It will be the sum of the two side numbers.
a●c b

5. Factor: x2 – 8x + 12 ax2 + bx + c 12 -2 -6 -8 a = 1 b = -8 c = 12
In this trinomial, what are the values of the variables a, b, and c? -8 b
a = 1 b = c = 12
To fill in the sides of the X figure you need to find two numbers that have a product of 12 and a sum of -8.
What would those numbers be?

6. a●c
Place the numbers from the sides of the X figure into your factored answer this way:
(x ) (x ) 12 -2 -6 -8
– 2
– 6 b
Side #
Side #
Check your answer by FOILing in your head. Look carefully at the sum of the Inner ∙ Inner + Outer ∙ Outer to check that their sum equals the middle term of the trinomial you just factored.
(x – 2) (x – 6)
= x2 – 6x – 2x + 12
= x2 – 8x + 12

7. (x ) (x ) – 7 + 3 Factor: x2 – 4x - 21 ax2 + bx + c -21 -7 3
In this trinomial, what are the values of the variables a, b, and c? -4 b
a = 1 b = c = -21
Find two numbers that have a product of -21 and a sum of -4.
(x ) (x )
– 7
+ 3
Side #
Side #
Check: (x - 7) (x + 3)
= x2 + 3x – 7x – 21 = x2 - 4x - 21

8. (x ) (x ) + 2 + 13 Factor: x2 + 15x + 26 ax2 + bx + c 26 2 13
In this trinomial, what are the values of the variables a, b, and c? 15 b
a = 1 b = c = 26
Find two numbers that have a product of 26 and a sum of 15.
(x ) (x )
+ 2
+ 13
Check: (x + 2) (x + 13)
= x2 + 13x + 2x = x2 + 15x + 26

9. (x ) (x ) + 2 - 3 Factor: x2 - x - 6 ax2 + bx + c -6 2 -3
In this trinomial, what are the values of the variables a, b, and c? -1 b
a = 1 b = c = -6
Find two numbers that have a product of -6 and a sum of -1.
(x ) (x )
+ 2
- 3
Check: (x + 2) (x - 3)
= x2 - 3x + 2x - 6 = x2 - x - 6

10. Find two monomials that have a product of 10y2 and a sum of 7y.
Factor: x2 + 7xy + 10y2
a●c
10y2
Think of it as: x2 + 7yx + 10y2 2y 5y
ax2 + bx + c 7y b
a = 1 b = 7y c = 10y2
Find two monomials that have a product of 10y2 and a sum of 7y.
(x ) (x )
+ 2y
+ 5y
Check: (x + 2y) (x + 5y)
= x2 + 5xy + 2xy + 10y2
= x2 + 7xy + 10y2

11. Time for 18 Practice Problems!