11.6 Solve by Factoring Using Square Roots
Name ___________________________
Learning Objective: A.SSE.2
I will rewrite an expression into factored form by square roots
A.SSE.3
I will find the factors of a quadratic function and then solve to find the zeros
A.APR.3
I will factor a quadratic function to determine the zeros
A.REI.4
I will solve a quadratic equation by factoring first by square roots
F.IF.8
I will use factoring to find the zeros of a quadratic function
Factor each polynomial, if possible. If the polynomial cannot be factored, write not factorable.
1. 225b2 − a2
2. 4a2 − 9b2
3. n2 – 121
4. 121m2 − 144p2
5. x2 + 22x + 121
6. 81 + 18j + j2
7. 25c2 − 10c + 1
8. r2 − 26r + 169
9. w2 − 9
10. 9t2 − 1
11. b2 − 256
12. 4m2 + 12m + 9
13. 2x2 – 2
14. −54a2 + 6
15. 4x2 − 12x + 9
16. 25b2 − 40b + 16
Factor each expression completely.
17. 12x – 18y
18. 25x3 + 50x2
19. 4x3 + 12x2 + 3x + 9
20. x2 – 10x + 25
21. x2 + 13x + 22
22. x2 + 4x – 32
Solve each quadratic equation by factoring and applying the Zero-Product Property.
23. 9a2 − 64 = 0
24. 4d2 − 1 = 0
25. 16x2 − 9 = 0
26. 25p2 − 16 = 0
27. 36q2 = 49
28. 3b2 = 27
29. x2 − 18x + 81 = 0
30. 4p2 + 4p + 1 = 0
31. 9g2 − 12g + 4 = 0
32. 9x2 − 6x + 1 = 0
33. 25k2 + 20k + 4 = 0
34. p2 + 2p + 1 = 0
35. w2 − 6w + 9 = 0
36. 9a2 + 12a + 4 = 0
37. 27h2 = 48
38. 75g2 = 147
Answers: 1. (15b + a)(15b – a) 3. (n + 11)(n – 11) 5. (x + 11)(x + 11) 7. (5c – 1)(5c – 1)
9. (w + 3)(w – 3) 11. (b + 16)(b – 16) 13. 2(x2 – 1), 2(x + 1)(x – 1) 15. (2x – 3)(2x – 3)
8
17. 6(2x – 3y) 19) (4x2 + 3)(x + 3) 21) (x + 11)(x + 2) 23. (3a + 8)(3a – 8) = 0, a = 
3
3
7
25. (4x + 3)(4x – 3) = 0, x = 
27. (6q + 7)(6q – 7) = 0, q = 
29. (x – 9)2 = 0, x = 9
4
6
2
2
31. (3g – 2)2 = 0, x =
33. (5x + 2)2 = 0, x = 
35. (x – 3)2 = 0, x = 3
5
3
4
37. 3(9h2 – 16), 3(3h + 4)(3h – 4), h = 
3