Intermediate Algebra
Skill Builder # PF 11
Factoring the Sum or Difference of Cubes
A polynomial is a sum of cubes if it looks like
a3 + b3
and it factors into
( a + b ) ( a2 ab + b 2 ) .
Likewise, the difference of cubes factors into
(
)
a3 b 3 = ( a b )
Intermediate Algebra Skill
Factoring the Sum or Difference of Cubes
Factor each completely.
1) x 3 + 8
2) a 3 + 64
3) a 3 + 216
4) 27 + 8 x 3
5) a 3 216
6) 64 x 3 27
7) 27m 3 125
8) x 3 64
9) 432 + 250m 3
10) 81 x 3 + 192
11) 500 x 3 + 256
12) 81 x 3 + 24
Intermediate Algebra
Skill Builder # PF - 5
Factoring Two-Variable Quadratic Trinomials with Leading Coefficient of 1
A two-variable quadratic trinomial with leading coefficient of 1 looks like
x
bxy
cy
To factor such a trinomial find two numbers that mul
Intermediate Algebra
Skill Builder # PF 7
Factoring Two-Variable Quadratic Trinomials with Leading Coefficient Different
from 1
Any Method
Examples
1. 40
31
35
Solution:
-31
Thus, 25 and -56
-56
are the two numbers that multiply to
and that add up to 31
Intermediate Algebra
Skill Builder # PF - 5
Factoring Two-Variable Quadratic Trinomials with Leading Coefficient of 1
A two-variable quadratic trinomial with leading coefficient of 1 looks like
x
bxy
cy
To factor such a trinomial find two numbers that mul
Intermediate Algebra
Skill-Builder # PF - 3
Finding Two Numbers that Multiply to One Number and Add Up to Another
Examples
1.
12
?
?
7
i
35
2.
5
i
35
9
?
?
9
11
i
-22
-2
i
-22
3.
-11
-11
?
-15
4
i
-60
?
i
-60
4.
-18
?
?
i
45
-18
-15
-3
i
45
Intermediate A