Download Math 8H

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
2
14
7
-2
-7
9
-9
-4
2 -2
0
56
-8
-7
-15
-33
-3 11
8
-2
6
-5
-3
Math 8H
8-3
Factoring Trinomials
x2 + bx + c
Algebra 1
Glencoe McGraw-Hill
JoAnn Evans
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.
ax2 + bx + c
a●c
b
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
12
-2 -6
-8
b
Factor:
x2 – 8x + 12
ax2 + bx + c
In this trinomial, what are the values of
the variables a, b, and c?
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?
a●c
12
-2 -6
-8
b
Place the numbers from the
sides of the X figure into your
factored answer this way:
(x – 2 ) (x – 6 )
Side #
Side #
Check your answer by FOILing in your
head. Look carefully at the sum of the
= x2 – 6x – 2x + 12
Inner ∙ Inner + Outer ∙ Outer
to check that their sum equals the
2
= x – 8x + 12
middle term of the trinomial you just
factored.
(x – 2) (x – 6)
a●c
-21
-7 3
-4
b
Factor:
x2 – 4x - 21
ax2 + bx + c
In this trinomial, what are the
values of the variables a, b, and c?
a=1
b = -4
c = -21
Find two numbers that have a
product of -21 and a sum of -4.
(x – 7 ) (x + 3 )
Side #
Side #
Check: (x - 7) (x + 3) = x2 + 3x – 7x – 21 = x2 - 4x - 21
a●c
26
2 13
15
b
Factor:
x2 + 15x + 26
ax2 + bx + c
In this trinomial, what are the
values of the variables a, b, and c?
a=1
b = 15
c = 26
Find two numbers that have a
product of 26 and a sum of 15.
(x + 2 ) (x + 13)
Check: (x + 2) (x + 13) = x2 + 13x + 2x + 26 = x2 + 15x + 26
a●c
-6
2 -3
-1
b
Factor:
x2 - x - 6
ax2 + bx + c
In this trinomial, what are the
values of the variables a, b, and c?
a=1
b = -1
c = -6
Find two numbers that have a
product of -6 and a sum of -1.
(x + 2) (x - 3 )
Check: (x + 2) (x - 3) = x2 - 3x + 2x - 6 = x2 - x - 6
a●c
10y2
2y
7y
b
Factor:
Think of it as:
5y
x2 + 7xy + 10y2
x2 + 7yx + 10y2
ax2 + bx + c
a=1
b = 7y
c = 10y2
Find two monomials that have a
product of 10y2 and a sum of 7y.
(x + 2y ) (x + 5y)
Check: (x + 2y) (x + 5y)
= x2 + 5xy + 2xy + 10y2
= x2 + 7xy + 10y2