Factoring Worksheet With Examples Page 25
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EXAMPLE
Factor a x
+ bx + c
Factor each trinomial.
2
a. 7 x
+ 29x + 4
In this trinomial, a = 7, b = 29, and c = 4. You need to find two numbers
with a sum of 29 and a product of 7 · 4 or 28. Make an organized list of
the factors of 28 and look for the pair of factors with the sum of 29.
Factors of 28
Sum of Factors
29
1,
28
The correct factors are 1 and 28.
2
2
7 x
+ 29x + 4 = 7 x
+ mx + nx + 4
Write the pattern.
2
= 7 x
+ 1x + 28x + 4
m = 1 and n = 28
2
= (7 x
+ 1x) + (28x + 4)
Group terms with common factors.
= x(7x + 1) + 4(7x + 1)
Factor the GCF from each grouping.
= (7x + 1)(x + 4)
Distributive Property
2
b. 10 x
- 43x + 28
In this trinomial, a = 10, b = -43 and c = 28. Since b is negative, m + n is
negative. Since c is positive, mn is positive. So, both m and n are negative.
Factors of 280
Sum of Factors
Finding Factors
-1, -280
-281
Put pairs in an
-2, -140
-142
List the negative
Look for the pairs
organized list so you
-4, -70
-74
factors of 10 · 28
of factors with a
do not miss any
or 280.
sum of -43.
possible pairs of
-5, -56
-61
factors.
-7, -40
-47
-43
-8,
-35
The correct factors are -8 and -35.
2
10 x
- 43x + 28
2
= 10 x
+ mx + nx + 28
Write the pattern.
2
= 10 x
+ (-8)x + (-35)x + 28
-
-
m =
8 and n =
35
2
= (10 x
- 8x) + (-35x + 28)
Group terms with common factors.
= 2x(5x - 4) + 7(-5x + 4)
Factor the GCF from each grouping.
= 2x(5x - 4) + 7(-1)(5x - 4)
-5x + 4 = (-1)(5x - 4)
= 2x(5x - 4) + (-7)(5x - 4)
7(-1) = -7
= (5x - 4)(2x - 7)
Distributive Property
2
c. 3 x
+ 24x + 45
Factoring
2
Completely
The GCF of the terms 3 x
, 24x, and 45 is 3. Factor this out first.
Always check for a
2
2
3 x
+ 24x + 45 = 3( x
+ 8x + 15)
Distributive Property
GCF first before trying
2
to factor a trinomial.
Now factor x
+ 8x + 15. Since the leading coefficient is 1, find two
factors of 15 with a sum of 8. The correct factors are 3 and 5.
2
So, x
+ 8x + 15 = (x + 3)(x + 5). Thus, the complete factorization of
2
+ 24x + 45 is 3(x + 3)(x + 5).
3 x
2
2
2
1
+ 13x + 6
1
+ 22x - 8
1
- 35y + 30
A.
5 x
B.
6 x
C.
10 y
442
Chapter 8 Factoring
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