# Factoring Trinomials-1

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```					Factoring Trinomials-1
Example: Solution: Factor: x2 – 7x + 12 x2 – 7x + 12 = (x )(x )

It is helpful to be aware of the following signed number pattern: To obtain a positive product between two numbers, the numbers must have the same sign – either both positive or both negative. Since the sum is negative, we are looking for two negative numbers whose product is +12 and whose sum is – 7. Possibilities: 1. (−4)(−3) = + 12 2. (−12)( −1) = + 12 3. (−6)( −2) = + 12 So, [(−4) + (−3)] [(−12) + (−1)] [(−6) + (−2)] = −7 = −13 = −8 YES NO NO

x2 – 7x + 12

=

(x – 3)(x – 4)

Factor the following trinomials into binomials: 1. x2 + 2x + 1 2. x2 − 5x − 24

3.

x2 + x − 30

4.

x2 − 4x + 4

5.

x2 − 13x + 36

6.

x2 + x − 72

7.

x2 + 3x − 10

8.

x2 + 9x + 8

9.

x2 − 12x + 20

10.

x2 + 15x + 54

11.

x2 − 6x + 9

12.

x2 + 2x − 8

13.

x2 + 6x − 72

14.

x2 − 11x − 26

15.

x2 − 12x + 11

16.

x2 + 5x + 6

17.

x2 − 10x − 39

18.

x2 + 3x − 40

19.

x2 + 11x + 28

20.

x2 + 3x − 4

21.

x2 − 2x − 48

22.

x2 − 5x − 14

23.

x2 − 8x + 16

24.

x2 + 6x + 8

1. 2. 3. 4. 5. 6.

(x + 1)(x + 1) (x − 8)(x + 3) (x + 6)(x − 5) (x − 2)(x − 2) (x − 9)(x − 4) (x + 9)(x − 8)

7. 8. 9. 10. 11. 12.

(x + 5)(x − 2) (x + 1)(x + 8) (x − 10)(x − 2) (x + 9)(x + 6) (x − 3)(x − 3) (x + 4)(x − 2)

13. 14. 15. 16. 17. 18.

(x + 12)(x − 6) (x − 13)(x + 2) (x − 11)(x − 1) (x + 2)(x + 3) (x − 13)(x + 3) (x + 8)(x − 5)

19. 20. 21. 22. 23. 24.

(x + 7)(x + 4) (x + 4)(x − 1) (x − 8)(x + 6) (x − 7)(x + 2) (x − 4)(x − 4) (x + 2)(x + 4)

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