Factoring Trinomials worksheets - Free Printable

I'll solve each trinomial factoring problem step by step.

1) x² + 11x + 18
Looking for two numbers that multiply to 18 and add to 11: 9 and 2
Final Answer: (x + 9)(x + 2)

2) x² + 2x - 99
Looking for two numbers that multiply to -99 and add to 2: 11 and -9
Final Answer: (x + 11)(x - 9)

3) x² - 2x - 35
Looking for two numbers that multiply to -35 and add to -2: -7 and 5
Final Answer: (x - 7)(x + 5)

4) -2x² - 11x - 9
Factor out -1 first: -(2x² + 11x + 9)
Looking for two numbers that multiply to 18 and add to 11: 9 and 2
Final Answer: -(2x + 9)(x + 1) or (-2x - 9)(x + 1)

5) x² - x - 20
Looking for two numbers that multiply to -20 and add to -1: -5 and 4
Final Answer: (x - 5)(x + 4)

6) x² - 64
This is a difference of squares: a² - b² = (a + b)(a - b)
Final Answer: (x + 8)(x - 8)

7) x² - 6x + 8
Looking for two numbers that multiply to 8 and add to -6: -4 and -2
Final Answer: (x - 4)(x - 2)

8) x² + 9x + 14
Looking for two numbers that multiply to 14 and add to 9: 7 and 2
Final Answer: (x + 7)(x + 2)

9) 4x² + 3x - 7
Using AC method: 4 × (-7) = -28
Looking for two numbers that multiply to -28 and add to 3: 7 and -4
Split middle term: 4x² + 7x - 4x - 7
Group: x(4x + 7) - 1(4x + 7)
Final Answer: (4x + 7)(x - 1)

10) x² - 12x + 20
Looking for two numbers that multiply to 20 and add to -12: -10 and -2
Final Answer: (x - 10)(x - 2)

11) x² - 5x - 6
Looking for two numbers that multiply to -6 and add to -5: -6 and 1
Final Answer: (x - 6)(x + 1)

12) x² - x - 90
Looking for two numbers that multiply to -90 and add to -1: -10 and 9
Final Answer: (x - 10)(x + 9)

13) -7x² - 9x - 2
Factor out -1: -(7x² + 9x + 2)
Looking for two numbers that multiply to 14 and add to 9: 7 and 2
Final Answer: -(7x + 2)(x + 1) or (-7x - 2)(x + 1)

14) x² - 2x - 35
Looking for two numbers that multiply to -35 and add to -2: -7 and 5
Final Answer: (x - 7)(x + 5)

15) x² + x - 30
Looking for two numbers that multiply to -30 and add to 1: 6 and -5
Final Answer: (x + 6)(x - 5)

16) x² - 2x - 99
Looking for two numbers that multiply to -99 and add to -2: -11 and 9
Final Answer: (x - 11)(x + 9)

17) x² + 16x + 63
Looking for two numbers that multiply to 63 and add to 16: 9 and 7
Final Answer: (x + 9)(x + 7)

18) x² - 18x + 80
Looking for two numbers that multiply to 80 and add to -18: -10 and -8
Final Answer: (x - 10)(x - 8)

19) x² + 15x + 56
Looking for two numbers that multiply to 56 and add to 15: 8 and 7
Final Answer: (x + 8)(x + 7)

20) x² - 8x + 7
Looking for two numbers that multiply to 7 and add to -8: -7 and -1
Final Answer: (x - 7)(x - 1)

21) x² + 17x + 72
Looking for two numbers that multiply to 72 and add to 17: 9 and 8
Final Answer: (x + 9)(x + 8)

22) x² + 19x + 88
Looking for two numbers that multiply to 88 and add to 19: 11 and 8
Final Answer: (x + 11)(x + 8)

23) x² + 3x - 4
Looking for two numbers that multiply to -4 and add to 3: 4 and -1
Final Answer: (x + 4)(x - 1)

24) x² - x - 30
Looking for two numbers that multiply to -30 and add to -1: -6 and 5
Final Answer: (x - 6)(x + 5)

25) x² + 16x + 63
Looking for two numbers that multiply to 63 and add to 16: 9 and 7
Final Answer: (x + 9)(x + 7)

26) x² + 9x + 14
Looking for two numbers that multiply to 14 and add to 9: 7 and 2
Final Answer: (x + 7)(x + 2)

27) 15x² + 10x - 5
Factor out GCF of 5: 5(3x² + 2x - 1)
Looking for two numbers that multiply to -3 and add to 2: 3 and -1
Final Answer: 5(3x - 1)(x + 1)

28) -12x² - 26x - 12
Factor out -2: -2(6x² + 13x + 6)
Looking for two numbers that multiply to 36 and add to 13: 9 and 4
Final Answer: -2(3x + 2)(2x + 3)

29) x² + 7x + 10
Looking for two numbers that multiply to 10 and add to 7: 5 and 2
Final Answer: (x + 5)(x + 2)

30) x² + 11x + 28
Looking for two numbers that multiply to 28 and add to 11: 7 and 4
Final Answer: (x + 7)(x + 4)