Download 8-A3 name__________________ Factor each trinomial using the

8-A3
Algebra 8H
name__________________
Factoring Trinomials
(when the Leading Coefficient is 1) Lesson 8-3
Factor each trinomial using the product/sum X method. Check by multiplying
the factors using FOIL. If the polynomial is not factorable, write PRIME.
1. y2 + 7y + 12
2. x2 + 12x - 48
3. x2 – 11xy + 18y2
4. x2 + 4xy – 45y2
5. x2 - x - 30
6. x2 – 15x + 35
7. x2 + 3xy – 54y2
8. y2 - 5y - 14
9. x2 - 9x + 14
10. 30 - 17x + x2
11. x2 + 4xy – 21y2
12. a2 + 19ab + 60b2
Define:
13.
Prime Numbers: _________________________________________
Composite Numbers: _____________________________________
14.
When factoring out the greatest common monomial factor your answer
will be the __________ of the ________ and the remaining factors.
15. A polynomial can be factored by grouping if all of the following are true:
(a) ____________________________________________________
(b) ____________________________________________________
(c) ____________________________________________________
Factor. Check by multiplying the factors. If the polynomial doesn’t factor,
write “prime.” Show your work on a piece of paper, staple the paper to this handout.
16. y2 - 13y + 12 ______________ 17. x2 + 7x – 18 ______________
18. y2 – 7y + 12
______________ 19. j2 – 7j + 10 _______________
20. y2 - 8y + 12
______________ 21. y2 – 11y – 12 _______________
22. r2 + 16r + 28 ______________ 23. y2 - 4y – 12 _______________
24. y2 + 12y + 36 ______________ 25. y2 - y – 12 ________________
26. h2 – 12h + 27 ______________ 27. x2 - 4x + 3 _______________
28. a2 + 4a – 32 ______________ 29. 1 + 8d + 7d2 _______________
30. w2 + 14w + 33 ______________ 31. d2 – 2d + 1 ________________
32. r2 – 13r + 22 ______________ 33. g2 + 7g + 49 _______________
34. p2 – 12p + 11 ______________ 35. b2 + 6b – 91 _______________
36. f2 – 10f + 16 ______________ 37. b2 + 14b + 45 ______________
38. n2 + 19n + 48 ______________ 39. a2 + 24a + 23 ______________
8-A3 Handout Key
16. (y – 12) (y – 1)
17. (x + 9) (x – 2)
1.
(y + 3) (y + 4)
2.
Prime
3.
(x – 9y) (x – 2y)
4.
(x + 9y) (x – 5y)
5.
(x – 6) (x + 5)
6.
Prime
7.
(x + 9y) (x – 6y)
8.
(y – 7) (y + 2)
25. (y + 3) (y – 4)
9.
(x – 7) (x – 2)
26. (h – 9) (h – 3)
18. (y – 3) (y – 4)
19. (j – 2) (j – 5)
20. (y – 2) (y – 6)
21. (y + 1) (y – 12)
22. (r + 14) (r + 2)
23. (y – 6) (y + 2)
24. (y + 6)2
10. (x – 15) (x – 2)
27. (x – 1) (x – 3)
11. (x + 7y) (x – 3y)
28. (a + 8) (a – 4)
12. (a + 4b) (a + 15b)
29. (7d + 1) (d + 1)
13. Prime numbers have only two
factors, 1 and itself.
Composite numbers have
more than 2 factors.
30. (w + 11) (w + 3)
14. product of the GCF
33. Prime
15. a. 4 or more terms.
b. Terms with common
factors can be grouped.
c. The two common binomial
factors are identical or are
additive inverses (• by -1)
of each other.
34. (p – 11) (p – 1)
31. (d – 1)2
32. (r – 11) (r – 2)
35. (b + 13) (b – 7)
36. (f – 8) (f – 2)
37. (b + 9) (b + 5)
38. (n + 16) (n + 3)
39. (a + 1) (a + 23)