1. Factoring Trinomials II-the ac-method

2. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Factoring Trinomials II-the ac-method

3. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
b. Factor x2 – x – 6 by grouping.
Factoring Trinomials II-the ac-method

4. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
3x – 3y + ax – ay Group them into two groups.
= (3x – 3y) + (ax – ay)
b. Factor x2 – x – 6 by grouping.
Factoring Trinomials II-the ac-method

5. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
3x – 3y + ax – ay Group them into two groups.
= (3x – 3y) + (ax – ay) Factor out the GCF of each group.
= 3(x – y) + a(x – y)
b. Factor x2 – x – 6 by grouping.
Factoring Trinomials II-the ac-method

6. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
3x – 3y + ax – ay Group them into two groups.
= (3x – 3y) + (ax – ay) Factor out the GCF of each group.
= 3(x – y) + a(x – y) Pull the factor (x – y) again.
= (3 + a)(x – y)
b. Factor x2 – x – 6 by grouping.
Factoring Trinomials II-the ac-method

7. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
3x – 3y + ax – ay Group them into two groups.
= (3x – 3y) + (ax – ay) Factor out the GCF of each group.
= 3(x – y) + a(x – y) Pull the factor (x – y) again.
= (3 + a)(x – y)
b. Factor x2 – x – 6 by grouping.
We write x2 – x – 6
= x2 – 3x + 2x – 6
Factoring Trinomials II-the ac-method

8. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
3x – 3y + ax – ay Group them into two groups.
= (3x – 3y) + (ax – ay) Factor out the GCF of each group.
= 3(x – y) + a(x – y) Pull the factor (x – y) again.
= (3 + a)(x – y)
b. Factor x2 – x – 6 by grouping.
We write x2 – x – 6
= x2 – 3x + 2x – 6 Put them into two groups
= (x2 – 3x) + (2x – 6) Take out the common factors
= x(x – 3) + 2(x – 3)
Factoring Trinomials II-the ac-method

9. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
3x – 3y + ax – ay Group them into two groups.
= (3x – 3y) + (ax – ay) Factor out the GCF of each group.
= 3(x – y) + a(x – y) Pull the factor (x – y) again.
= (3 + a)(x – y)
b. Factor x2 – x – 6 by grouping.
We write x2 – x – 6
= x2 – 3x + 2x – 6 Put them into two groups
= (x2 – 3x) + (2x – 6) Take out the common factors
= x(x – 3) + 2(x – 3) Take out the common (x – 3)
= (x – 3)(x + 2)
Factoring Trinomials II-the ac-method

10. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
3x – 3y + ax – ay Group them into two groups.
= (3x – 3y) + (ax – ay) Factor out the GCF of each group.
= 3(x – y) + a(x – y) Pull the factor (x – y) again.
= (3 + a)(x – y)
b. Factor x2 – x – 6 by grouping.
We write x2 – x – 6
= x2 – 3x + 2x – 6 Put them into two groups
= (x2 – 3x) + (2x – 6) Take out the common factors
= x(x – 3) + 2(x – 3) Take out the common (x – 3)
= (x – 3)(x + 2)
Factoring Trinomials II-the ac-method
?

11. Some four terms formulas may be factored by the
grouping method, i.e. pulling out twice.
Example A.
a. Factor 3x – 3y + ax – ay by grouping.
3x – 3y + ax – ay Group them into two groups.
= (3x – 3y) + (ax – ay) Factor out the GCF of each group.
= 3(x – y) + a(x – y) Pull the factor (x – y) again.
= (3 + a)(x – y)
b. Factor x2 – x – 6 by grouping.
We write x2 – x – 6
= x2 – 3x + 2x – 6 Put them into two groups
= (x2 – 3x) + (2x – 6) Take out the common factors
= x(x – 3) + 2(x – 3) Take out the common (x – 3)
= (x – 3)(x + 2)
We use the ac-method to write trinomials into four-term
formulas for grouping.
Factoring Trinomials II-the ac-method
?

12. ac-Method:
Factoring Trinomials II-the ac-method

13. ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
Factoring Trinomials II-the ac-method
Example B. Factor 3x2 – 4x – 20 using the ac-method.

14. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac,
Factoring Trinomials II-the ac-method

15. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac,
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60.
Factoring Trinomials II-the ac-method

16. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60.
Factoring Trinomials II-the ac-method

17. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Factoring Trinomials II-the ac-method

18. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Here are two searching methods
-by the X-table,
or a regular table.
Factoring Trinomials II-the ac-method

19. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Here are two searching methods
-by the X-table,
or a regular table.
Factoring Trinomials II-the ac-method
–60
–4
1 60
u v
2, ,303,
15,12,45,
, 20,

20. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Here are two searching methods
-by the X-table,
or a regular table.
Factoring Trinomials II-the ac-method
–60
–4
1 60
u v
2, ,303, , 20,
15,12,45,

21. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Here are two searching methods
-by the X-table,
or a regular table.
Factoring Trinomials II-the ac-method
–60
–4
1 60
u v
2, ,303, , 20,
15,12,
10
45,
6

22. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Here are two searching methods
-by the X-table,
or a regular table.
Factoring Trinomials II-the ac-method
u v
1 60
2 30
3 20
4 15
5 12
6 10
–60
–4
1 60
u v
2, ,303, , 20,
15,12,
10
45,
6

23. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Here are two searching methods
-by the X-table,
or a regular table.
Factoring Trinomials II-the ac-method
u v
1 60
2 30
3 20
4 15
5 12
6 10
6*(–10) = – 60
6 + (–10) = –4
–60
–4
1 60
u v
2, ,303, , 20,
15,12,
10
45,
6

24. Example B. Factor 3x2 – 4x – 20 using the ac-method.
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
2. Write ax2 + bx + c as ax2 + ux + vx +c
then use the grouping method to factor (ax2 + ux) + (vx + c).
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Here are two searching methods
-by the X-table,
or a regular table.
Factoring Trinomials II-the ac-method
u v
1 60
2 30
3 20
4 15
5 12
6 10
6*(–10) = – 60
6 + (–10) = –4
–60
–4
1 60
u v
2, ,303, , 20,
15,12,
10
45,
6

25. Example B. Factor 3x2 – 4x – 20 using the ac-method.
Because a = 3, c = –20, we’ve
ac = 3(–20) = –60. We need
two numbers u and v such that
uv = –60 and u + v = –4.
Here are two searching methods
-by the X-table,
or a regular table.
Factoring Trinomials II-the ac-method
u v
1 60
2 30
3 20
4 15
5 12
6 10
6*(–10) = – 60
6 + (–10) = –4
–60
–4
1 60
u v
2, ,303, , 20,
15,12,
10
45,
6
ac-Method: We assume that there is no common factor for
the trinomial ax2 + bx + c.
1. Calculate ac, and find two numbers u and v such that
uv is ac, and u + v = b.
2. Write ax2 + bx + c as ax2 + ux + vx +c
then use the grouping method to factor (ax2 + ux) + (vx + c)
If step 1 can’t be done, then the expression is prime.

26. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20
u v
1 60
2 30
3 20
4 15
5 12
6 10
6*(–10) = – 60
6 + (–10) = –4
Factoring Trinomials II-the ac-method

27. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20)
u v
1 60
2 30
3 20
4 15
5 12
6 10
6*(–10) = – 60
6 + (–10) = –4
Factoring Trinomials II-the ac-method

28. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2)
u v
1 60
2 30
3 20
4 15
5 12
6 10
6*(–10) = – 60
6 + (–10) = –4
Factoring Trinomials II-the ac-method

29. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2) pull out common factor
= (3x – 10)(x + 2)
Factoring Trinomials II-the ac-method

30. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2) pull out common factor
= (3x – 10)(x + 2)
Example C.
Factor 3x2 – 6x – 20 by the ac-method, if possible.
If it’s prime, use a table to justify your answer.
Factoring Trinomials II-the ac-method

31. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2) pull out common factor
= (3x – 10)(x + 2)
Example C.
Factor 3x2 – 6x – 20 by the ac-method, if possible.
If it’s prime, use a table to justify your answer.
a = 3, c = –20, hence ac = 3(–20) = –60.
Factoring Trinomials II-the ac-method

32. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2) pull out common factor
= (3x – 10)(x + 2)
Example C.
Factor 3x2 – 6x – 20 by the ac-method, if possible.
If it’s prime, use a table to justify your answer.
a = 3, c = –20, hence ac = 3(–20) = –60.
We need two numbers u and v such that
uv = –60 and u + v = –6.
Factoring Trinomials II-the ac-method

33. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2) pull out common factor
= (3x – 10)(x + 2)
Example C.
Factor 3x2 – 6x – 20 by the ac-method, if possible.
If it’s prime, use a table to justify your answer.
a = 3, c = –20, hence ac = 3(–20) = –60.
We need two numbers u and v such that
uv = –60 and u + v = –6.
u v
1 60
2 30
3 20
4 15
5 12
6 10
Factoring Trinomials II-the ac-method

34. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2) pull out common factor
= (3x – 10)(x + 2)
Example C.
Factor 3x2 – 6x – 20 by the ac-method, if possible.
If it’s prime, use a table to justify your answer.
a = 3, c = –20, hence ac = 3(–20) = –60.
We need two numbers u and v such that
uv = –60 and u + v = –6.
u v
1 60
2 30
3 20
4 15
5 12
6 10
Factoring Trinomials II-the ac-method
After examining all possible pairs of
u's and v’s, we see that no such
u and v exists.
no u and v such that
uv = –60 and u + v = –6.

35. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2) pull out common factor
= (3x – 10)(x + 2)
Example C.
Factor 3x2 – 6x – 20 by the ac-method, if possible.
If it’s prime, use a table to justify your answer.
a = 3, c = –20, hence ac = 3(–20) = –60.
We need two numbers u and v such that
uv = –60 and u + v = –6.
u v
1 60
2 30
3 20
4 15
5 12
6 10
Factoring Trinomials II-the ac-method
After examining all possible pairs of
u's and v’s, we see that no such
u and v exists.
no u and v such that
uv = –60 and u + v = –6.Hence 3x2 – 6x – 20 must be prime.

36. In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
Factoring Trinomials II-the ac-method

37. In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
Factoring Trinomials II-the ac-method

38. Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial ax2 + bx + c is factorable.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
Factoring Trinomials II-the ac-method

39. Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial ax2 + bx + c is factorable.
Otherwise, it is not factorable.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
Factoring Trinomials II-the ac-method

40. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

41. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2)
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

42. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

43. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24 = 73 is not a square,
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

44. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24 = 73 is not a square,
hence it is prime.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

45. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24 = 73 is not a square,
hence it is prime.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
b. 3x2 – 7x + 2
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

46. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24 = 73 is not a square,
hence it is prime.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
b. 3x2 – 7x + 2
b2 – 4ac = (–7)2 – 4(3)(2)
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

47. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24 = 73 is not a square,
hence it is prime.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
b. 3x2 – 7x + 2
b2 – 4ac = (–7)2 – 4(3)(2) = 49 – 24
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

48. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24 = 73 is not a square,
hence it is prime.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
b. 3x2 – 7x + 2
b2 – 4ac = (–7)2 – 4(3)(2) = 49 – 24 = 25 which is a squared
number,
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

49. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24 = 73 is not a square,
hence it is prime.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
b. 3x2 – 7x + 2
b2 – 4ac = (–7)2 – 4(3)(2) = 49 – 24 = 25 which is a squared
number, hence it is factorable.
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

50. Example D. Use the b2 – 4ac to see if the trinomial is
factorable. If it is, factor it.
a. 3x2 – 7x – 2
b2 – 4ac = (–7)2 – 4(3)(–2) = 49 + 24 = 73 is not a square,
hence it is prime.
In this section we give a formula that enables us to tell if a
trinomial is factorable or not.
This formula is an outcome of the quadratic formula.
b. 3x2 – 7x + 2
b2 – 4ac = (–7)2 – 4(3)(2) = 49 – 24 = 25 which is a squared
number, hence it is factorable.
In fact 3x2 – 7x + 2 = (3x – 1)(x – 2)
Factoring Trinomials II-the ac-method
Theorem: If b2 – 4ac = 0, 1, 4, 9, 16, 25, 36, .. i.e. is a
squared number, then the trinomial is factorable.
Otherwise, it is not factorable.

51. Write 3x2 – 4x – 20
= 3x2 + 6x –10x – 20 put in two groups
= (3x2 + 6x ) + (–10x – 20) pull out common factor
= 3x(x + 2) – 10 (x + 2) pull out common factor
= (3x – 10)(x + 2)
Example C. Factor 3x2 – 6x – 20 using the ac-method, if
possible.
a = 3, c = –20, hence ac = 3(-20) = –60.
We need two numbers u and v such that
uv = –60 and u + v = –6.
After searching all possibilities
we found that it's impossible.
Hence 3x2 – 6x – 20 is prime.
Factoring Trinomials II-the ac-method

52. 1. 3x2 – x – 2 2. 3x2 + x – 2 3. 3x2 – 2x – 1
4. 3x2 + 2x – 1 5. 2x2 – 3x + 1 6. 2x2 + 3x – 1
8. 2x2 – 3x – 27. 2x2 + 3x – 2
15. 6x2 + 5x – 6
10. 5x2 + 9x – 2
B. Factor. Factor out the GCF, the “–”, and arrange the
terms in order first.
9. 5x2 – 3x – 2
12. 3x2 – 5x + 211. 3x2 + 5x + 2
14. 6x2 – 5x – 613. 3x2 – 5x + 2
16. 6x2 – x – 2 17. 6x2 – 13x + 2 18. 6x2 – 13x – 2
19. 6x2 + 7x + 2 20. 6x2 – 7x + 2 21. 6x2 – 13x + 6
22. 6x2 + 13x + 6 23. 6x2 – 5x – 4 24. 6x2 – 13x + 8
25. 6x2 – 13x – 8 25. 4x2 – 9 26. 4x2 – 49
27. 25x2 – 4 28. 4x2 + 9 29. 25x2 + 9
30. – 6x2 – 5xy + 6y2 31. – 3x2 + 2x3– 2x 32. –6x3 – x2 + 2x
33. –15x3 – 25x2 – 10x 34. 12x3y2 –14x2y2 + 4xy2
Exercise A. Use the ac–method, factor the trinomial or
demonstrate that it’s not factorable.
Factoring Trinomials II-the ac-method