Factoring Trinomials
2
x + bx + c
CORD Math
Mrs. Spitz
Fall 2006
Objectives
• Students will learn how to factor
trinomials with the following pattern:
x2 + bx + c
Assignment
• Worksheets as provided
What does a factored trinomial look like?
(x + 3 )(x + 9 )
Look at the trinomial. Are the signs
positive, negative or both positive and
negative. For example:
x2 + 12x + 27
What are the
factors of 27
that add to
give you 12?
1 + 27 = 28
3 + 9 = 12
Both signs are positive meaning you are looking for factors of 27
that add to give you 12—the number in the middle. With no
coefficient (the number in front of the variable x2 (the letter), it’s
pretty easy to figure out.
Factor x2 +14x + 45
14
5
+
What are the
factors of 45 that
add to give you
14?
1 + 45 = 46
9
3 + 15 = 18
5 + 9 = 14
45
Format of factored
trinomial is:
(x + 5)(x + 9)
Trinomials—Let’s try this out!
• Tri meaning three
referring to the
number of terms
Examples:
x  22 x  21
2
t  2t  63
2
m  9a  20
2
r  4r  21
2
What does a factored trinomial look like?
(x + 1 )(x +
21 )
Look at the trinomial. Are the signs
positive, negative or both positive and
negative. For example:
x2 + 22x + 21
What are the
factors of 21
that add to
give you 22?
1 + 21 = 22
3 + 7 = 10
Both signs are positive meaning you are looking for factors of 21
that add to give you 22—the number in the middle. With no
coefficient (the number in front of the variable x2 (the letter), it’s
pretty easy to figure out.
Factor t2 – 2t – 63
What are the
With two negatives, you are looking for a positive
factors of 63 that
and a negative number to multiply to give you a
subtract to give
negative 63.
you -2?
-2
7
-63
1 - 63 = -62
9
3 – 21 = -18
7 - 9 = -2
Format of factored
trinomial is:
(t + 7)(t - 9)
Factor m2 – 9m + 20
What are the
With a negative in front and a positive in back, youfactors of 20 that
are looking for two negative factors that add to give
you negative 9 and multiply to give a positive 20. add to give you
20?
-9
-4
20
-1 – 20 = -21
5
-2 – 10 = -12
-4 – 5 = -9
Format of factored
trinomial is:
(m - 4)(m - 5)
Factor r2 + 4r - 21
(r + 7 )(r - 3)
Look at the trinomial. The first is
positive, the second negative meaning
you are looking for factors of 21 that
subtract to give you a positive 4.
What are the
factors of 21
that subtract to
give you 4?
21 - 1 = 20
7–3=4
Format of factored
trinomial is:
(r + 7)(r - 3)