Factoring Worksheet With Examples Page 18
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50EXAMPLE
b and c are Positive
2
+ 6x + 8.
Factor x
In this trinomial, b = 6 and c = 8. You need to find two numbers with a
sum of 6 and a product of 8. Make an organized list of the factors of 8, and
look for the pair of factors with a sum of 6.
Factors of 8 Sum of Factors
1, 8
9
2,
4
6
The correct factors are 2 and 4.
2
x
+ 6x + 8 = (x + m)(x + n)
Write the pattern.
= (x + 2)(x + 4)
m = 2 and n = 4
CHECK
You can check this result by multiplying the two factors.
F
O
I
L
2
(x + 2)(x + 4) = x
+ 4x + 2x + 8
FOIL method
2
= x
+ 6x + 8
Simplify.
Factor each trinomial.
2
2
1
1
A.
a
+ 8a + 15
B.
9 + 10t + t
When factoring a trinomial where b is negative and c is positive, use
what you know about the product of binomials to narrow the list of possible
factors.
EXAMPLE
b is Negative and c is Positive
2
- 10x + 16.
Factor x
In this trinomial, b = -10 and c = 16. This means that m + n is negative
and mn is positive. So m and n must both be negative. Make a list of the
negative factors of 16, and look for the pair with the sum of -10.
Factors of 16 Sum of Factors
-1, -16
-17
Testing Factors
-2,
-8
-10
Once you find the
-4, -4
-8
The correct factors are -2 and -8.
correct factors, there is
2
no need to test any
x
- 10x + 16 = (x + m)(x + n)
Write the pattern.
other factors.
= (x
-
-
2)(x
8)
m = -2 and n = -8
Therefore, it is not
necessary to test -4
CHECK
You can check this result by using a
and -4 in Example 2.
graphing calculator. Graph
2
y = x
- 10x + 16 and y = (x - 2)(x - 8)
on the same screen. Since only one graph
appears, the two graphs must coincide.
Therefore, the trinomial has been
factored correctly.
[ 10, 10 ] scl: 1 by [ 10, 10 ] scl: 1
Factor each trinomial.
2
2
2
21 - 22m + m
2
- 11s + 28
A.
B.
s
2
435
Lesson 8-3 Factoring Trinomials: x
+ bx + c
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