Math 8H

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
8
9
-4
56
6
2
-2
-8
-7
-2
-3
0
-15
-5
2
Math 8H
8-3 Factoring Trinomials x2 bx c
Algebra 1 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 well factor quadratic trinomials that have
a leading coefficient of 1. Theyll look like
this ax2 bx c. The number that replaces
the variable a will always be 1 in this lesson.
4
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
a?c
ax2 bx c
12
-2
-6
In this trinomial, what are the values of the
variables a, b, and c?
-8
b
a 1 b -8 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
6
2
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
Factor x2 4x - 21
a?c
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 -4 c -21
Find two numbers that have a product of
-21 and a sum of -4.
(x ) (x )
3
7
Side
Side
Check (x - 7) (x 3)
x2 3x 7x 21 x2 - 4x - 21
8
Factor x2 15x 26
a?c
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 15 c 26
Find two numbers that have a product of
26 and a sum of 15.
(x ) (x )
13
2
Check (x 2) (x 13)
x2 13x 2x 26 x2 15x 26
9
Factor x2 - x - 6
a?c
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 -1 c -6
Find two numbers that have a product of
-6 and a sum of -1.
(x ) (x )
- 3
2
Check (x 2) (x - 3)
x2 - 3x 2x - 6 x2 - x - 6
10
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 )
5y
2y
x2 5xy 2xy 10y2 x2 7xy 10y2
Check (x 2y) (x 5y)
11
Time for 18 Practice Problems!