MAT 0024 Ch 13 Factoring Review Worksheet Instructor: C. St.Denis
Page 2 of 4
)2)(2(2
)4(2
82
3
23
35
−+
=−
=−
xxx
xx
xx
Step 1: Factor out greatest common factor )2(
3
x
Step 2: Determine if the remaining binomial is the difference of
two squares
Step 2: It is the difference of two squares
(skip steps 3-4)
Step 5: Can it be factored further? No
22
22
234
)3(3
)96(3
27183
−
=+−
=+−
xx
xxx
xxx
Step 1: Factor out greatest common factor )3(
2
x
Step 2: Determine if the remaining binomial is the difference of
two squares: NOT binomial.
Step 3: Determine if the remaining trinomial is a perfect square:
It seems to be
2
)3( −x
Step 5: Can it be factored further? No
)12)(43(
)12)(4()12(3
)48()36(
4836
4116
2
2
2
−−
=−−+−
=+−+−
=+−−
=+−
aa
aaa
aaa
aaa
aa
Step 2: Not a binomial
Step 3: Not a perfect square; factor by AC method (or trial &
error).
a. Find the product of ac (24).
b. Find two numbers whose product is ac (24) and whose
sum is b (-11). The two numbers are -8 and -3.
c. Rewrite the trinomial so the middle term is the sum of
the two numbers found as coefficients.
Step 4: Factor by grouping.
Step 5: Cannot be factored further.
)8)(3(
)8(3)8(
)243()8(
2438
++
=+++
=+++
yx
yyx
yxxy
yxxy
Step 4: Factor by grouping
a. group two terms together
b. find GCF of each group
c. Use distributive property to “pull out” the common
term.
d. Rewrite as product of two binomials
Step 5: Cannot be factored further
)14(2
282
23
345
++
=++
bbab
ababab
Step 1: Find GCF (
3
2ab )
Skip step 2 (not a binomial remaining)
Step 3-4: Not a perfect square and can’t be factored.
Step 5: Cannot be factored further.
)2)(3(
65
2
++
=++
xx
xx
Step 3: Not a perfect square, coefficient of first term is 1, so just
reverse FOIL:
a. First two terms are x and x
b. Last two terms have to multiply to be 6 and sum to be
5. The two numbers are 2 and 3.
c. Both signs need to be positive
Step 4: Check the OI term to make sure it’s correct. It is.