FACTORING POLYNOMIALS

6. (x3 + y3) = (x + y)(x2 – xy + y2 )

7. 1. Factor x3 + 8
1. Find the cube roots of the first and
last terms
8
x3
First Term: = x
Second Term: = 2

8. 1. Factor x 3 + 8
2. Write their sum as the first
factor.
(x + 2)

9. 1. Factor x 3 + 8
3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Subtracting the product of the first
and second terms of the first factor; c.
Squaring the last term of the first factor
(x + 2) ( )
x2 -2x + 4

10. Factor 8a3 + 64
1. Find the cube roots of the first and
last terms?
64
8a3
First Term: = 2
Second Term: = 4
a

11. 2. Write their sum as the first
factor.
(2a + 4)
Factor 8a3 + 64

12. 3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Subtracting the product of the first
and second terms of the first factor; c.
Squaring the last term of the first factor
(2a + 4)( )
4a2 -8a + 16
Factor 8a3 + 64

13. Factor 27a6 + 216b3
1. Find the cube roots of the first and
last terms?
216b3
27a6
First Term: = 3
Second Term: = 6
a2
b

14. 2. Write their sum as the first
factor.
Factor 27a6 + 216b3
3a2 + 6b

15. 3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Subtracting the product of the first
and second terms of the first factor; c.
Squaring the last term of the first factor
( )
9a4-18a2b
3a2 + 6b + 36b2
Factor 27a6 + 216b3

16. (x3 - y3) = (x - y)(x2 + xy + y2 )

17. Factor x 3 - 8
1. Find the cube roots of the first and
last terms?
8
x 3
First Term: = x
Second Term: = 2

18. Factor x 3 - 8
2. Write their difference as the
first factor.
(x - 2)

19. Factor x 3 + 8
3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Adding the product of the first and
second terms of the first factor; c. Squaring
the last term of the first factor
(x - 2) ( )
x2 + 2x + 4

20. Factor 8a3 - 64
1. Find the cube roots of the first and
last terms?
64
8a3
First Term: = 2
Second Term: = 4
a

21. 2. Write their sum as the first
factor.
(2a - 4)
Factor 8a3 - 64

22. 3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Subtracting the product of the first
and second terms of the first factor; c.
Squaring the last term of the first factor
(2a - 4) ( )
4a2 +8a+ 16
Factor 8a3 - 64

23. 1. Find the cube roots of the first and last terms
2. Write their sum as the first factor.
3. For the second factor, get the trinomial factor
by:
a. Squaring the first term of the first factor;
b. Subtracting the product of the first and second
terms of the first factor;
c. Squaring the last term of the first factor

24. Find the Factors of the following
1. b3 - 343 2. 8c3 + 125
3. 8m3 - 729 4. 8a3 + 64b3