Chapter R. Section 4
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C. Bellomo, revised 26-Aug-07
Section R.4 โ Factoring
Common Factors:
โข Common Factors occur when there is a factor that is common to all terms in the expression
โข What are the common factors in the expression below?
22 3
525
843
x
x
yxyxy
+
++
Grouping:
โข When you have two or more elements in an expression with common factors, you can group them
together and factor the common factors out
โข This doesn't happen all too often in 'real life'
โข Does the expression below have common factors? Can you factor by grouping?
32
22yy yโ+โ
Factoring Quadratics: (2
ax bx c++
)
โข If a = 1
1. The solution will be of the form ()()xxยฑยฑ
, and your goal is to find what goes inside the
boxes along with the signs in front of them
2. Look at the sign of c
โ if it is plus then you have the same sign (both plus or both minus). Keep in mind sum
โ if it is different then you have opposite signs. Keep in mind difference
3. Identify the factors of c
โ find the factors whose sum (or difference) is b
โ place these values in the boxes
โ be careful with the difference, as the larger value should have the sign of b
โข Example. Factor 2215ttโโ
c = โ15, so the signs are different
The factors of 15 are 1*15, and 3*5
We are looking for the difference of those factors to be 2, so we choose 3*5
Since we want the difference to be negative, we choose โ5 and 3
(x โ 5)(x + 3)
โข If 1aโ
1. Be sure that you can't factor out a constant term
2. Well, there is a method for factoring when it is in this form, but it often causes frustration on
the part of every student, so just use the quadratic formula
3. The formula will yield two values 24
2
bb ac
a
โยฑ โ , and you factor accordingly
