Factoring
ax
2
+ bx + c
when a ≠ 1
When factoring problems such as
1)
6x
2
17x – 14
2)
5x
2
– 14x + 8
3)
8x
2
+ 38x
+ 9
I like to factor these by grouping. Trial and error works if you see it right off. If not, it can waste time and build
frustration. Factor by grouping is no fail assuming you do the math correct.
Let’s take a look at the first problem.
1)
6x
2
17x – 14
Step 1: Multiply “a” and “c” which are 6 and 14
6 * 14 = 84
Step 2: Look for factors of 84 (‘ac’) that add to ‘b’ which is 17.
Factors of 84
add to
17
1
84
83
1
84
83
2
42
40
2
42
40
3
28
25
3
28
25
4
21
17
4
21
17
6
14
8
6
14
8
7
12
5
7
12
5
That’s all the factors of 84. How did I get those? I simply grabbed my calculator and started dividing 84 by 2, 3, 4, …
until I got repeats which was at 12. What do I mean by that. When I divided by 8, 9, 10, and 11 I had decimals. 12 went
evenly, but I already have 12 listed with 7.
Step 3: Now you don’t have to list all the factors because we can stop when we get to the ones that will add up to 17. It is
important however, to list your factors in order.
So we found 4 and 21 to give us the 17. At this point we will take our question and rewrite the 17x into +4x – 21x. So
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 Spring '09
 RANJITREBELLO
 Factoring

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