Here is a summary of what to remember as you factor polynomials.
Practice and Problem-Solving Exercises
A Practice
See Problem 1.
Find the GCF of the first two terms and the GCF of the last two terms for each polynomial.
-
2
z
3
+
6
z
2
+
3
z
+
9
2 z cubed , plus , 6 z squared , plus 3 z plus 9
-
10
g
3
−
25
g
2
+
4
g
−
10
10 g cubed , minus , 25 g squared , plus 4 g minus 10
-
2
r
3
+
12
r
2
−
5
r
−
30
2 r cubed , plus , 12 r squared , minus 5 r minus 30
-
6
p
3
+
3
p
2
+
2
p
+
1
6 p cubed , plus , 3 p squared , plus 2 p plus 1
Factor each expression.
-
15
q
3
+
40
q
2
+
3
q
+
8
15 q cubed , plus , 40 q squared , plus 3 q plus 8
-
14
y
3
+
8
y
2
+
7
y
+
4
14 y cubed , plus , 8 y squared , plus 7 y plus 4
-
14
z
3
−
35
z
2
+
16
z
−
40
14 z cubed , minus , 35 z squared , plus 16 z minus 40
-
11
w
3
−
9
w
2
+
11
w
−
9
11 w cubed , minus , 9 w squared , plus 11 w minus 9
-
8
m
3
+
12
m
2
−
2
m
−
3
8 m cubed , plus , 12 m squared , minus 2 m minus 3
-
12
k
3
−
27
k
2
−
40
k
+
90
12 k cubed , minus , 27 k squared , minus 40 k plus 90
-
20
v
3
+
24
v
2
−
25
v
−
30
20 v cubed , plus , 24 v squared , minus 25 v minus 30
-
18
h
3
+
45
h
2
−
8
h
−
20
18 h cubed , plus , 45 h squared , minus 8 h minus 20
-
12
y
3
+
4
y
2
−
9
y
−
3
12 y cubed , plus , 4 y squared , minus 9 y minus 3