11.5 Factor and Solve by using Diamonds
Name _______________________
Learning Objective: A.SSE.2 I will rewrite a trinomial with a coefficient of 1 into factored form
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 with a trinomial with a coefficient of 1
F.IF.8
I will use factoring to find the zeros of a quadratic function
Use “Diamonds” to factor.
1.
2.
-
-
18
9. x2 + 14x + 45
4.
18
63
7
-
16
8
6. x2 – 5x + 6
7. x2 + 7x + 12
8. n2 – 10n + 21
11. x2 – 11x + 28
12. x2 + 13x + 22
17
5. x2 – 10x + 24
3.
3
10. x2 – 18x + 17
13. x2 + 16x + 28
14. n2 – 16n + 48
15. x2 + 3x – 4
16. n2 + n – 20
17. x2 – 16x – 36
18. x2 + 4x – 21
19. x2 + 6x – 27
20. x2 – 3x – 28
Write the simplified expression for the area for each figure.
x–4
5x – 2
21.
22.
3x
Area = ___________
4x + 1
Area = ___________
3x – 2
23.
3x – 2
Area = ___________
Solve each problem by factoring first, and then solving each factor.
24. x2 – 11x + 30 = 0
25. x2 + 6x – 16 = 0
26. x2 + 17x + 30 = 0
27. x2 – 10x + 9 = 0
28. x2 + 11x + 24 = 0
29. x2 + 4x – 12 = 0
30. 3x2 + 9x – 12 = 0
31. 2x2 – 14x + 12 = 0
32. 3x2 – 15x – 72 = 0
33. 4x2 – 32x + 48 = 0
34. 2x2 – 4x – 30 = 0
35. 4x2 + 24x + 32 = 0
Answers: 1) (x + 18)(x – 1) 3) (x + 9)(x + 7) 5) (x – 4)(x – 6) 7) (x + 3)(x + 4) 9) (x + 9)(x + 5)
11) (x – 7)(x – 4) 13) (x + 14)(x + 2) 15) (x + 4)(x – 1) 17) (x – 18)(x + 2)
19) (x + 9)(x – 3) 21) 15x2 – 6x 23) 9x2 – 12x + 4 25) (x + 8)(x – 2) = 0, x = –8, x = 2
27) (x – 9)(x – 1) = 0, x = 9, x = 1 29) (x + 6)(x – 2) = 0, x = –6, x = 2
31) 2(x2 – 7x + 6) = 0, 2(x – 6)(x – 1) = 0, x = 6, x = 1
33) 4(x2 – 8x + 12) = 0, 4(x – 6)(x – 2) = 0, x = 6, x = 2
35) 4(x2 + 6x + 8) = 0, 4(x + 4)(x + 2) = 0, x = –4, x = –2