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### 5 2factoring trinomial i

1. 1. Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. Factoring Trinomials and Making Lists
2. 2. Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Factoring Trinomials and Making Lists
3. 3. Factoring Trinomials and Making Lists Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible,
4. 4. Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) Factoring Trinomials and Making Lists
5. 5. Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 Factoring Trinomials and Making Lists
6. 6. Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. Factoring Trinomials and Making Lists
7. 7. Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 Factoring Trinomials and Making Lists
8. 8. Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 6 = (2)(3) we have that Factoring Trinomials and Making Lists
9. 9. Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 we have that 5 = 2+3 6 = (2)(3) Factoring Trinomials and Making Lists
10. 10. So if (x + u)(x + v) = x2 + ux + vx + uv = x2 + (u + v)x + uv Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 we have that 5 = 2+3 6 = (2)(3) Factoring Trinomials and Making Lists
11. 11. So if (x + u)(x + v) = x2 + ux + vx + uv = x2 + (u + v)x + uv is to be Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 we have that 5 = 2+3 6 = (2)(3) = x2 + bx + c Factoring Trinomials and Making Lists
12. 12. So if (x + u)(x + v) = x2 + ux + vx + uv = x2 + (u + v)x + uv is to be Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 we must have that uv = c, we have that 5 = 2+3 6 = (2)(3) = x2 + bx + c Factoring Trinomials and Making Lists
13. 13. So if (x + u)(x + v) = x2 + ux + vx + uv = x2 + (u + v)x + uv is to be Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 we must have that uv = c, and u + v = b. we have that 5 = 2+3 6 = (2)(3) = x2 + bx + c Factoring Trinomials and Making Lists
14. 14. So if (x + u)(x + v) = x2 + ux + vx + uv = x2 + (u + v)x + uv is to be Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 we must have that uv = c, and u + v = b. In other words, to factor the trinomial x2 + bx + c, look for a pair of numbers u and v such that uv = c, and u + v = b. we have that 5 = 2+3 6 = (2)(3) = x2 + bx + c Factoring Trinomials and Making Lists
15. 15. So if (x + u)(x + v) = x2 + ux + vx + uv = x2 + (u + v)x + uv is to be Trinomials (three-term) are polynomials of the form ax2 + bx + c where a, b, and c are numbers. The product of two binomials is a trinomials: (#x + #)(#x + #)  ax2 + bx + c Hence, to factor a trinomial, we write the trinomial as a product of two binomials, if possible, that is: ax2 + bx + c  (#x + #)(#x + #) We start with the case a = 1, trinomials of the form x2 + bx + c. When multiplying (x + 2)(x + 3) = x2 + 5x + 6 we must have that uv = c, and u + v = b. In other words, to factor the trinomial x2 + bx + c, look for a pair of numbers u and v such that uv = c, and u + v = b. If no such pair of u and v exist, the trinomial is prime (not factorable). we have that 5 = 2+3 6 = (2)(3) = x2 + bx + c Factoring Trinomials and Making Lists
16. 16. Example A. a. Factor x2 + 5x + 6 Factoring Trinomials and Making Lists Factoring the trinomial x2 + bx + c
17. 17. Example A. a. Factor x2 + 5x + 6 Factoring Trinomials and Making Lists Factoring the trinomial x2 + bx + c To factor the trinomial x2 + bx + c, search for a pair of numbers u and v such that uv = c, and u + v = b.
18. 18. Example A. a. Factor x2 + 5x + 6 We want (x + u)(x + v) = x2 + 5x + 6, so we need u and v where uv = 6 and u + v = 5. Factoring Trinomials and Making Lists Factoring the trinomial x2 + bx + c To factor the trinomial x2 + bx + c, search for a pair of numbers u and v such that uv = c, and u + v = b.
19. 19. Example A. a. Factor x2 + 5x + 6 We want (x + u)(x + v) = x2 + 5x + 6, so we need u and v where uv = 6 and u + v = 5. Factoring Trinomials and Making Lists Factoring the trinomial x2 + bx + c To factor the trinomial x2 + bx + c, search for a pair of numbers u and v such that uv = c, and u + v = b. To carry this out, make a list of all the possible u and v such that uv = c,
20. 20. Example A. a. Factor x2 + 5x + 6 We want (x + u)(x + v) = x2 + 5x + 6, so we need u and v where uv = 6 and u + v = 5. List all such u and v where uv = 6: (1)(6) = (2)(3) = (-1)(-6) = (-2)(-3) = 6 Factoring Trinomials and Making Lists Factoring the trinomial x2 + bx + c To factor the trinomial x2 + bx + c, search for a pair of numbers u and v such that uv = c, and u + v = b. To carry this out, make a list of all the possible u and v such that uv = c,
21. 21. Example A. a. Factor x2 + 5x + 6 We want (x + u)(x + v) = x2 + 5x + 6, so we need u and v where uv = 6 and u + v = 5. List all such u and v where uv = 6: (1)(6) = (2)(3) = (-1)(-6) = (-2)(-3) = 6 Factoring Trinomials and Making Lists Factoring the trinomial x2 + bx + c To factor the trinomial x2 + bx + c, search for a pair of numbers u and v such that uv = c, and u + v = b. To carry this out, make a list of all the possible u and v such that uv = c, then search for the pair that satisfies u + v = b. Such a pair of u and v may or may not exist.
22. 22. Example A. a. Factor x2 + 5x + 6 We want (x + u)(x + v) = x2 + 5x + 6, so we need u and v where uv = 6 and u + v = 5. List all such u and v where uv = 6: (1)(6) = (2)(3) = (-1)(-6) = (-2)(-3) = 6 Factoring Trinomials and Making Lists Factoring the trinomial x2 + bx + c To factor the trinomial x2 + bx + c, search for a pair of numbers u and v such that uv = c, and u + v = b. To carry this out, make a list of all the possible u and v such that uv = c, then search for the pair that satisfies u + v = b. Such a pair of u and v may or may not exist. 2, 3 is the pair where u + v = 5.
23. 23. Example A. a. Factor x2 + 5x + 6 We want (x + u)(x + v) = x2 + 5x + 6, so we need u and v where uv = 6 and u + v = 5. List all such u and v where uv = 6: (1)(6) = (2)(3) = (-1)(-6) = (-2)(-3) = 6 so x2 + 5x + 6 = (x + 2)(x + 3). Factoring Trinomials and Making Lists Factoring the trinomial x2 + bx + c To factor the trinomial x2 + bx + c, search for a pair of numbers u and v such that uv = c, and u + v = b. To carry this out, make a list of all the possible u and v such that uv = c, then search for the pair that satisfies u + v = b. Such a pair of u and v may or may not exist. 2, 3 is the pair where u + v = 5.
24. 24. c. Factor x2 + 5x – 6 We want (x + u)(x + v) = x2 + 5x – 6, so we need uv = –6 and u + v = 5. Since -6 = (–1)(6) = (1)(–6) = (–2)(3) =(2)(–3) and –1 + 6 = 5, so x2 + 5x – 6 = (x – 1)(x + 6). b. Factor x2 – 5x + 6 We want (x + u)(x + v) = x2 – 5x + 6, so we need u and v where uv = 6 and u + v = –5. Since 6 = (1)(6) = (2)(3) = (-1)(-6) = (-2)(-3) and –2 – 3 = –5, so x2 – 5x + 6 = (x – 2)(x – 3). Example A. a. Factor x2 + 5x + 6 We want (x + u)(x + v) = x2 + 5x + 6, so we need u and v where uv = 6 and u + v = 5. Since 6 = (1)(6) = (2)(3) = (-1)(-6) = (-2)(-3) and 2x + 3x = 5x, so x2 + 5x + 6 = (x + 2)(x + 3) Factoring Trinomials and Making Lists
25. 25. Using the X-Table For Listing Factoring the trinomial x2 + bx + c The task of searching for a pair of numbers u and v such that uv = c, and u + v = b for the purpose of factoring x2 + bx + c, requires a systematic reach of all the possible u and v.
26. 26. Using the X-Table For Listing Factoring the trinomial x2 + bx + c The task of searching for a pair of numbers u and v such that uv = c, and u + v = b for the purpose of factoring x2 + bx + c, requires a systematic reach of all the possible u and v. To do this, we use the X-table as shown. the X-table for (factoring) x2 + bx + c
27. 27. Using the X-Table For Listing Factoring the trinomial x2 + bx + c The task of searching for a pair of numbers u and v such that uv = c, and u + v = b for the purpose of factoring x2 + bx + c, requires a systematic reach of all the possible u and v. To do this, we use the X-table as shown. the X-table for (factoring) x2 + bx + c Place c here Place b here c b
28. 28. Using the X-Table For Listing Factoring the trinomial x2 + bx + c The task of searching for a pair of numbers u and v such that uv = c, and u + v = b for the purpose of factoring x2 + bx + c, requires a systematic reach of all the possible u and v. To do this, we use the X-table as shown. the X-table for (factoring) x2 + bx + c Place c here Place b here list orderly the u’s and v's where uv = c and check if u + v = b. u v c b
29. 29. Using the X-Table For Listing Factoring the trinomial x2 + bx + c The task of searching for a pair of numbers u and v such that uv = c, and u + v = b for the purpose of factoring x2 + bx + c, requires a systematic reach of all the possible u and v. To do this, we use the X-table as shown. the X-table for (factoring) x2 + bx + c Place c here Place b here the X-table for x2 – 14x – 72 list orderly the u’s and v's where uv = c and check if u + v = b. u v c b
30. 30. Using the X-Table For Listing Factoring the trinomial x2 + bx + c The task of searching for a pair of numbers u and v such that uv = c, and u + v = b for the purpose of factoring x2 + bx + c, requires a systematic reach of all the possible u and v. To do this, we use the X-table as shown. the X-table for (factoring) x2 + bx + c Place c here Place b here the X-table for x2 – 14x – 72 – 72 Place c here list orderly the u’s and v's where uv = c and check if u + v = b. u v c b
31. 31. Using the X-Table For Listing Factoring the trinomial x2 + bx + c The task of searching for a pair of numbers u and v such that uv = c, and u + v = b for the purpose of factoring x2 + bx + c, requires a systematic reach of all the possible u and v. To do this, we use the X-table as shown. the X-table for (factoring) x2 + bx + c Place c here Place b here the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = c and check if u + v = b. u v c b
32. 32. Using the X-Table For Listing Factoring the trinomial x2 + bx + c The task of searching for a pair of numbers u and v such that uv = c, and u + v = b for the purpose of factoring x2 + bx + c, requires a systematic reach of all the possible u and v. To do this, we use the X-table as shown. the X-table for (factoring) x2 + bx + c Place c here Place b here the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = c and check if u + v = b. u v c b list orderly the u’s and v's where uv = – 72 and check if u + v = b.
33. 33. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b.
34. 34. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. – 72 –14 1 72 u v
35. 35. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. – 72 –14 1 72 u v
36. 36. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. – 72 –14 1 72 u v 2, ,36
37. 37. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. – 72 –14 1 72 u v 2, ,363, , 24
38. 38. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. – 72 –14 1 72 u v 2, ,363, , 244, ,18
39. 39. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. Since +4 –18 = –14 and 4(–18) = –72 so we have the u and v and that x2 – 14x – 72 = (x – 18)(x + 4). – 72 –14 1 72 u v 2, ,363, , 244, ,18
40. 40. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. Since +4 –18 = –14 and 4(–18) = –72 so we have the u and v and that x2 – 14x – 72 = (x – 18)(x + 4). Example B. Use the X-table to factor x2 – 14x – 72 or verify that it’s prime. – 72 –14 1 72 u v 2, ,363, , 244, ,18
41. 41. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. Since +4 –18 = –14 and 4(–18) = –72 so we have the u and v and that x2 – 14x – 72 = (x – 18)(x + 4). – 72 –14 1 72 u v 2, ,363, , 244, ,18 Example B. Use the X-table to factor x2 – 14x – 72 or verify that it’s prime. – 72 –14u v the X-table of x2 – 14x – 72 is:
42. 42. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. Since +4 –18 = –14 and 4(–18) = –72 so we have the u and v and that x2 – 14x – 72 = (x – 18)(x + 4). – 72 –14 1 72 u v 2, ,363, , 244, ,18 Example B. Use the X-table to factor x2 – 14x – 72 or verify that it’s prime. – 72 –14 1 72 u v 2, ,363, , 244, ,18 the X-table of x2 – 14x – 72 is: ,126,8, , 9 check that:
43. 43. Using the X-Table For Listing the X-table for Place b here x2 – 14x – 72 – 72 Place c here –14 list orderly the u’s and v's where uv = – 72 and check if u + v = b. – 72 –14 1 72 u v 2, ,363, , 244, ,18 Since +4 –18 = –14 and 4(–18) = –72 so we have the u and v and that x2 – 14x – 72 = (x – 18)(x + 4). the X-table of x2 – 14x – 72 is: ,126,8, , 9 – 72 –14 1 72 u v 2, ,363, , 244, ,18 Example B. Use the X-table to factor x2 – 14x – 72 or verify that it’s prime. After listing all u’s and v’s and we see that no such u and v exist, we conclude that x2 – 14x – 7 is prime. check that:
44. 44. Observations About Signs Factoring Trinomials and Making Lists
45. 45. Observations About Signs Given that x2 + bx + c = (x + u)(x + v) so that uv = c, we observe the following. Factoring Trinomials and Making Lists
46. 46. Observations About Signs Given that x2 + bx + c = (x + u)(x + v) so that uv = c, we observe the following. 1. If c is positive, then u and v have same sign. In particular, if b is also positive, then both are positive. Factoring Trinomials and Making Lists
47. 47. Observations About Signs Given that x2 + bx + c = (x + u)(x + v) so that uv = c, we observe the following. 1. If c is positive, then u and v have same sign. In particular, if b is also positive, then both are positive. From the examples above x2 + 5x + 6 = (x + 2)(x + 3) Factoring Trinomials and Making Lists
48. 48. Observations About Signs Given that x2 + bx + c = (x + u)(x + v) so that uv = c, we observe the following. 1. If c is positive, then u and v have same sign. In particular, if b is also positive, then both are positive. if b is negative, then both are negative. From the examples above x2 + 5x + 6 = (x + 2)(x + 3) Factoring Trinomials and Making Lists
49. 49. { Observations About Signs Given that x2 + bx + c = (x + u)(x + v) so that uv = c, we observe the following. 1. If c is positive, then u and v have same sign. In particular, if b is also positive, then both are positive. if b is negative, then both are negative. From the examples above x2 + 5x + 6 = (x + 2)(x + 3) x2 – 5x + 6 = (x – 2)(x – 3) Factoring Trinomials and Making Lists
50. 50. { Observations About Signs Given that x2 + bx + c = (x + u)(x + v) so that uv = c, we observe the following. 1. If c is positive, then u and v have same sign. In particular, if b is also positive, then both are positive. if b is negative, then both are negative. From the examples above x2 + 5x + 6 = (x + 2)(x + 3) x2 – 5x + 6 = (x – 2)(x – 3) 2. If c is negative, then u and v have opposite signs. Factoring Trinomials and Making Lists
51. 51. { Observations About Signs Given that x2 + bx + c = (x + u)(x + v) so that uv = c, we observe the following. 1. If c is positive, then u and v have same sign. In particular, if b is also positive, then both are positive. if b is negative, then both are negative. From the examples above x2 + 5x + 6 = (x + 2)(x + 3) x2 – 5x + 6 = (x – 2)(x – 3) 2. If c is negative, then u and v have opposite signs. The one with larger absolute value has the same sign as b. Factoring Trinomials and Making Lists
52. 52. { Observations About Signs Given that x2 + bx + c = (x + u)(x + v) so that uv = c, we observe the following. 1. If c is positive, then u and v have same sign. In particular, if b is also positive, then both are positive. if b is negative, then both are negative. From the examples above x2 + 5x + 6 = (x + 2)(x + 3) x2 – 5x + 6 = (x – 2)(x – 3) 2. If c is negative, then u and v have opposite signs. The one with larger absolute value has the same sign as b. From the example above x2 – 5x – 6 = (x – 6)(x + 1) Factoring Trinomials and Making Lists
53. 53. Example C. a. Factor x2 + 4x – 12 We need u and v having opposite signs such that uv = –12, u + v = +4. Since -12 = (-1)(12) = (-2)(6) = (-3)(4)… They must be –2 and 6 hence x2 + 4x – 12 = (x – 2)(x + 6). b. Factor x2 – 8x – 12 We need u and v such that uv = –12, u + v = –8 with u and v having opposite signs. This is impossible. Hence x2 – 8x – 12 is prime. Factoring Trinomials and Making Lists
54. 54. Exercise. A. Factor. If it’s prime, state so. 1. x2 – x – 2 2. x2 + x – 2 3. x2 – x – 6 4. x2 + x – 6 5. x2 – x + 2 6. x2 + 2x – 3 7. x2 + 2x – 8 8. x2 – 3x – 4 9. x2 + 5x + 6 10. x2 + 5x – 6 13. x2 – x – 20 11. x2 – 5x – 6 12. x2 – 5x + 6 17. x2 – 10x – 24 14. x2 – 8x – 20 15. x2 – 9x – 20 16. x2 – 9x + 20 18. x2 – 10x + 24 19. x2 – 11x + 24 20. x2 – 11x – 24 21. x2 – 12x – 36 22. x2 – 12x + 36 23. x2 – 13x – 36 24. x2 – 13x + 36 B. Factor. Factor out the GCF, the “–”, and arrange the terms in order first if necessary. 29. 3x2 – 30x – 7227. –x2 – 5x + 14 28. 2x3 – 18x2 + 40x 30. –2x3 + 20x2 – 24x 25. x2 – 36 26. x2 + 36 31. –2x4 + 18x2 32. –3x – 24x3 + 22x2 33. 5x4 + 10x5 – 5x3 Factoring Trinomials and Making Lists
55. 55. 35. –3x3 – 30x2 – 48x34. –yx2 + 4yx + 5y 36. –2x3 + 20x2 – 24x 40. 4x2 – 44xy + 96y2 37. –x2 + 11xy + 24y2 38. x4 – 6x3 + 36x2 39. –x2 + 9xy + 36y2 C. Factor. Factor out the GCF, the “–”, and arrange the terms in order first. D. Factor. If not possible, state so. 41. x2 + 1 42. x2 + 4 43. x2 + 9 43. 4x2 + 25 44. What can you conclude from 41–43? Factoring Trinomials and Making Lists