Factoring General Quadratic Trinomials

4. 1 . 21
3 . 7

5. -1 . -
40-8 . -
5
-4 . -10
-2 . -
20

8. 1 . 30
6 x 5 =30
2 . 15
3 . 10
5 . 6

9. -1 . 24
12 x -2 = -
24
-2 . 12
-3 . 8
-4 . 6

10. 𝒙 𝟐 − 𝟓𝒙 + 𝟔
𝟔𝒙 𝟐 − 𝟑𝟒𝒙 + 𝟐𝟎

11. 𝒙 𝟐
+ 𝟔𝒙 + 𝟓
5= 1.5
=𝒙 𝟐
+(1+5)x+5
= 𝒙 𝟐
+ 𝒙 + 𝟓𝒙 + 𝟓
=(𝒙 𝟐
+x)+(5x+5)
=x(x+1)+5(x+1)
=(x+1)(x+5)

12. 𝒙 𝟐 − 𝟓𝒙 + 𝟔
6=-2.-3
=𝒙 𝟐
+ −𝟐 + −𝟑 𝐱 + 𝟔
=𝒙 𝟐
-2x-3x+6
=(𝒙 𝟐
-2x)+(-3x+6)
=x(x-2)+(-3)(x-2)
=(x-2)(x-3)

13. 𝟐𝟏𝒙 𝟐
− 𝒙 − 𝟐
21.-2=-42=6.-7
=21𝒙 𝟐
+ 𝟔 − 𝟕 𝐱 − 𝟐
=21𝒙 𝟐
+6x-7x-2
=(21𝒙 𝟐
-7x)+(6x-2)
=7x(3x-1)+2(3x-1)
=(3x-1)(7x+2)

14. 𝟔𝒙 𝟐
− 𝟑𝟒𝒙 + 𝟐𝟎
6.20=120=-30.-4
=6𝒙 𝟐
+(-30-4)x+20
=6𝒙 𝟐
-30x-4x+20
=(6𝒙 𝟐
− 𝟑𝟎𝐱) + (−𝟒𝐱 + 𝟐𝟎)
=6x(x-5)+(-4)(x-5)
=(x-5)(6x-4)

15. 𝟕𝒎 𝟐 + 𝟔𝒎 − 𝟏
7.-1=-7=7.-1
=𝟕𝒎 𝟐
+(7-1)m-1
=𝟕𝒎 𝟐
+7m-m-1
=(𝟕𝒎 𝟐
+7m)+(-m-1)
=7m(m+1)+(-1)(m+1)
=(m+1)(7m-1)

16. 𝟖𝒏 𝟐 + 𝟕𝟏𝒏 − 𝟗𝟎
8.-90=-720=-9.80
=𝟖𝒏 𝟐
+(-9+80)n-90
=𝟖𝒏 𝟐
-9n+80n-90
=(𝟖𝒏 𝟐
−𝟗𝒏) + (𝟖𝟎𝒏 − 𝟗𝟎)
=n(8n-9)+10(8n-9)
=(8n-9)(n+10)

17. Seatwork: Factor the ff. completely.
1. 𝒙 𝟐 − 𝟒𝒙 − 𝟕𝟕
𝟐. 𝒙 𝟐 + 𝟓𝒙 − 𝟏𝟎𝟒
𝟑. 𝒚 𝟐
+ 𝟕𝒚 − 𝟏𝟒𝟒
𝟒. 𝒙 𝟐 + 𝟏𝟎𝒙 + 𝟐𝟒
𝟓. 𝒙 𝟐 + 𝟏𝟑𝒙 + 𝟒𝟎
𝟔. 𝟏𝟐𝒙 𝟐 + 𝟓𝒙 − 𝟐
𝟕. 𝟑𝒙 𝟐 − 𝟑𝒙 − 𝟗𝟎
𝟖. 𝟏𝟓𝒙 𝟐
+ 𝟏𝟒𝒙 − 𝟖
𝟗. 𝟔𝒙 𝟐 − 𝟏𝟏𝒙 + 𝟒
𝟏𝟎. 𝟗𝒙 𝟐 + 𝟏𝟐𝒙 + 𝟒

18. Seatwork: Factor the ff. completely.
1. 𝒙 𝟐 − 𝟒𝒙 − 𝟕𝟕
-77=-11.7
=𝒙 𝟐
+(-11+7)x-77
=𝒙 𝟐
-11x+7x-77
=( 𝒙 𝟐 − 𝟏𝟏𝒙) + (𝟕𝒙 − 𝟕𝟕)
=x(x-11)+7(x-11)
=(x-11)(x+7)

19. Seatwork: Factor the ff. completely.
𝟐. 𝒙 𝟐 + 𝟓𝒙 − 𝟏𝟎𝟒
-104=-8.13
=𝒙 𝟐
+(-8+13)x-104
=𝒙 𝟐
-8x+13x-104
=( 𝒙 𝟐 − 𝟖𝒙) + (𝟏𝟑𝒙 − 𝟏𝟎𝟒)
=x(x-8)+13(x-8)
=(x-8)(x+13)

20. Seatwork: Factor the ff. completely.
𝟑. 𝒚 𝟐 + 𝟕𝒚 − 𝟏𝟒𝟒
-144=-9.16
=𝒚 𝟐
+(-9+16)y-144
=𝒚 𝟐
− 𝟗𝒚 + 𝟏𝟔𝒚 − 𝟏𝟒𝟒
=(𝒚 𝟐
+ 𝟏𝟔𝒚) + (−𝟗𝒚 − 𝟏𝟒𝟒)
=y(y+16)+(-9)(y+16)
=(y+16)(y-9)

21. Seatwork: Factor the ff. completely.
𝟒. 𝒙 𝟐 + 𝟏𝟎𝒙 + 𝟐𝟒
24=6.4
=𝒙 𝟐
+(6+4)x+24
=𝒙 𝟐
+6x+4x+24
=( 𝒙 𝟐 + 𝟔𝒙) + (𝟒𝒙 + 𝟐𝟒)
=x(x+6)+4(x+6)
=(x+6)(x+4)

22. Seatwork: Factor the ff. completely.
𝟓. 𝒙 𝟐 + 𝟏𝟑𝒙 + 𝟒𝟎
40=5.8
=𝒙 𝟐
+(5+8)x+40
=𝒙 𝟐
+5x+8x+40
=( 𝒙 𝟐 + 𝟓𝒙) + (𝟖𝒙 + 𝟒𝟎)
=x(x+5)+8(x+5)
=(x+5)(x+8)

23. Seatwork: Factor the ff. completely.
𝟔. 𝟏𝟐𝒙 𝟐 + 𝟓𝒙 − 𝟐
12.-2=-24=-3.8
=12𝒙 𝟐
+(-3+8)x-2
=12𝒙 𝟐
-3x+8x-2
=(𝟏𝟐 𝒙 𝟐 − 𝟑𝒙) + (𝟖𝒙 − 𝟐)
=3x(4x-1)+2(4x-1)
=(4x-1)(3x+2)

24. Seatwork: Factor the ff. completely.
𝟕. 𝟑𝒙 𝟐 − 𝟑𝒙 − 𝟗𝟎
3.-90=-270=-18.15
=3𝒙 𝟐
+ −𝟏𝟖 + 𝟏𝟓 𝒙 − 𝟗𝟎
=3𝒙 𝟐
-18x+15x-90
=(𝟑 𝒙 𝟐 − 𝟏𝟖𝒙) + (𝟏𝟓𝒙 − 𝟗𝟎)
=3x(x-6)+15(x-6)
=(x-6)(3x+15)

25. Seatwork: Factor the ff. completely.
𝟖. 𝟏𝟓𝒙 𝟐 + 𝟏𝟒𝒙 − 𝟖
15.-8=-120=20.-6
=15𝒙 𝟐
+(20-6)x-8
=15𝒙 𝟐
+20x-6x-8
=(𝟏𝟓 𝒙 𝟐 + 𝟐𝟎𝒙) + (−𝟔𝒙 − 𝟖)
=5x(3x+4)+(-2)(3x+4)
=(3x+4)(5x-2)

26. Seatwork: Factor the ff. completely.
𝟗. 𝟔𝒙 𝟐 − 𝟏𝟏𝒙 + 𝟒
6.4=24=-8.-3
=6𝒙 𝟐
+(-8-3)x+4
=6𝒙 𝟐
-8x-3x+4
=(𝟔 𝒙 𝟐 − 𝟖𝒙) + (−𝟑𝒙 + 𝟒)
=2x(3x-4)+(-1)(3x-4)
=(3x-4)(2x-1)

27. Seatwork: Factor the ff. completely.
𝟏𝟎. 𝟗𝒙 𝟐 + 𝟏𝟐𝒙 + 𝟒
9.4=36=6.6
=9𝒙 𝟐
+(6+6)x+4
=9𝒙 𝟐
+6x+6x+4
=(𝟗 𝒙 𝟐 + 𝟔𝒙) + (𝟔𝒙 + 𝟒)
=3x(3x+2)+2(3x+2)
=(3x+2)(3x+2)

28. Assignment:
Answer all the skill builder
pages 15 and 18, and Math
Skill Milestone letters A and
B page 19-20.

29. Determine the binomial factors.
𝟏. 𝒙 𝟐 + 𝟏𝟏𝒙 + 𝟐𝟖
28 = 1.28 2.14 4.7
= 𝒙 𝟐 + 𝟒 + 𝟕 𝒙 + 𝟐𝟖
= 𝒙 𝟐
+ 𝟒𝒙 + 𝟕𝒙 + 𝟐𝟖
= (𝒙 𝟐
+𝟒𝒙) + (𝟕𝒙 + 𝟐𝟖)
= 𝒙 (𝒙 + 𝟒) + 𝟕 (𝒙 + 𝟒)
= (𝒙 + 4)(𝒙 + 7)

30. Determine the binomial factors.
𝟐. 𝒚 𝟐 + 𝟏𝟔𝒚 + 𝟔𝟑
63 = 1.63 3.21 7.9
= 𝒚 𝟐 + 𝟕 + 𝟗 𝒚 + 𝟔𝟑
= 𝒚 𝟐
+ 𝟕𝒚 + 𝟗𝒚 + 𝟔𝟑
= (𝒚 𝟐
+𝟕𝒚) + (𝟗𝒚 + 𝟔𝟑)
= 𝒚 (𝒚 + 𝟕) + 𝟗 (𝒚 + 𝟕)
= (y + 7) (y + 9)

31. What can be said about the factors of
𝒑 𝟐
+ 𝟏𝟎𝒑 + 𝟐𝟓 𝑎𝑛𝑑 𝒑 𝟐
− 𝟏𝟎𝒑 + 𝟐𝟓?
• 𝒑 𝟐 + 𝟏𝟎𝒑 + 𝟐𝟓
=(p + 5) (p + 5)
• 𝒑 𝟐
− 𝟏𝟎𝒑 + 𝟐𝟓
=(p + 5) (p - 5)

32. Determine the factors of the ff.
𝟏. 𝟖𝒗 𝟐 + 𝟐𝟔𝒗 + 𝟏𝟓
8. = 1.120 2.60 4.30
= 𝟖𝒗 𝟐 + 𝟔 + 𝟐𝟎 𝒗 + 𝟏𝟓
= 𝟖𝒗 𝟐 + 𝟔𝒗 + 𝟐𝟎𝒗 + 𝟏𝟓
= (𝟖𝒗 𝟐
+𝟔𝒗) + (𝟐𝟎𝒗 + 𝟏𝟓)
= 𝟐𝒗(𝟒𝒗+ 𝟑) + 𝟓(𝟒𝒗+ 𝟑)
= (4v + 3)(𝟐𝒗 + 5)
15= 120 3.40 5.24 6.20
8.14
10.12

33. Determine the factors of the ff.
𝟏. 𝟒𝒖 𝟐 − 𝟓𝒖 − 𝟔
4. = 1.-242.-12 4.-6
= 𝟒𝒖 𝟐 + 𝟑 − 𝟖 𝒖 −𝟔
= 𝟒𝒖 𝟐 + 𝟑𝒖−𝟖𝒖 −𝟔
= (𝟒𝒖 𝟐
+𝟑𝒖) + (−𝟖𝒖 − 𝟔)
= 𝒖 (𝟒𝒖+ 𝟑) + (−𝟐)(𝟒𝒖+ 𝟑)
= (4u + 3)(𝒖 − 𝟐)
-6= -24 3.-8

34. a. Express the polynomials as factors.

35. a. Express the polynomials as factors.

36. a. Express the polynomials as factors.

37. a. Express the polynomials as factors.