Download Factor Trinomials of the Form ax2+bx+c

Math 90
5.4 "Factoring General Trinomials"
Objectives:
Factor trinomials of the form ax2 + bx + c where a 6= 1:
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Factor perfect-square trinomials.
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Use the grouping method to factor trinomials.
Factor Trinomials of the Form ax2+bx+c
The FOIL Method:
To factor ax2 + bx + c; a 6= 1, using the FOIL method:
1: Factor out the GCF, if one exists.
2: Find two First terms whose product is ax2 :
3: Find two Last terms whose product is c:
4: Look for Outer and Inner products resulting from steps (2) and (3) for which the sum is bx:
5: Check by multiplying.
Example 1: (Factoring ax2 + bx + c by using the FOIL method)
Factor.
a) 3x2
10x
8
b) 24x2
76x + 40
Another method for factoring trinomials of the type ax2 + bx + c; a 6= 1; involves the product, ac, of the leading
coe¢ cient a and the last term c. It is called the ac method. Because it uses factoring by grouping, it is also referred to as
the grouping method.
The ac-Method:
To factor a trinomial by grouping
1.
Factor out any GCF.
2.
Identify a; b; and c, and …nd the key number ac:
3.
Find two integers whose product is the key number ac and whose sum is b:
4.
Express the middle term, bx; as the sum (or di¤erence) of the numbers from step 3.
5.
Enter the two numbers found in step 4 as coe¢ cients of x in the form shown below.
6.
Factor the equivalent four-term polynomial by grouping.
Page: 1
Notes by Bibiana Lopez
Beginning and Intermediate Algebra by Gustafson and Frisk
5.4
Example 2: (Factoring ax2 + bx + c by using the ac-method)
Factor the following trinomials.
a) 5x2 + 7x + 2
c)
6x2
e) 25a2 b
15x
b) 3p2
6
40ab + 10b
4p
4
d) 4 + 11a2 + 6a4
f) 15a2 + 17ab
Page: 2
4b2
Notes by Bibiana Lopez
Beginning and Intermediate Algebra by Gustafson and Frisk
5.4
Factoring Perfect-Square Trinomials
Example 3: (Factoring perfect-square trinomials)
Factor the following trinomials.
a) 9x2
c) 9
b) 4x2
12x + 4
4x2
4xy
y2
d) 16
Page: 3
20x + 25
a2
2ab
b2
Notes by Bibiana Lopez