Quadratic expressions worksheet for factoring practice.

It looks like you've uploaded a worksheet with 20 quadratic expressions that need to be factored. The task is likely to factor each quadratic expression into two binomials.

Let’s go through each one step by step, using factoring techniques (such as finding two numbers that multiply to the constant term and add to the coefficient of the middle term).

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Factoring Strategy:

For a quadratic in the form $ x^2 + bx + c $, we look for two numbers that:
- Multiply to $ c $
- Add to $ b $

Then write the expression as $ (x + m)(x + n) $, where $ m $ and $ n $ are those numbers.

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Now let's solve all 20:

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1. $ x^2 - 4x - 45 $
→ Find two numbers that multiply to $-45$, add to $-4$:
$-9$ and $5$: $(-9)(5) = -45$, $-9 + 5 = -4$
→ $ (x - 9)(x + 5) $

2. $ x^2 - 5x - 6 $
→ Multiply to $-6$, add to $-5$: $-6$ and $1$
→ $ (x - 6)(x + 1) $

3. $ x^2 - 17x + 72 $
→ Multiply to $72$, add to $-17$: $-8$ and $-9$
→ $ (x - 8)(x - 9) $

4. $ x^2 - 36 $
→ Difference of squares: $ x^2 - 6^2 $
→ $ (x - 6)(x + 6) $

5. $ x^2 + 7x - 8 $
→ Multiply to $-8$, add to $7$: $8$ and $-1$
→ $ (x + 8)(x - 1) $

6. $ x^2 - 3x - 54 $
→ Multiply to $-54$, add to $-3$: $-9$ and $6$
→ $ (x - 9)(x + 6) $

7. $ x^2 + 3x + 2 $
→ Multiply to $2$, add to $3$: $1$ and $2$
→ $ (x + 1)(x + 2) $

8. $ x^2 + 3x - 18 $
→ Multiply to $-18$, add to $3$: $6$ and $-3$
→ $ (x + 6)(x - 3) $

9. $ x^2 + 17x + 72 $
→ Multiply to $72$, add to $17$: $8$ and $9$
→ $ (x + 8)(x + 9) $

10. $ x^2 + 10x + 24 $
→ Multiply to $24$, add to $10$: $4$ and $6$
→ $ (x + 4)(x + 6) $

11. $ x^2 - 9x + 8 $
→ Multiply to $8$, add to $-9$: $-8$ and $-1$
→ $ (x - 8)(x - 1) $

12. $ x^2 + x - 42 $
→ Multiply to $-42$, add to $1$: $7$ and $-6$
→ $ (x + 7)(x - 6) $

13. $ x^2 - x - 72 $
→ Multiply to $-72$, add to $-1$: $-9$ and $8$
→ $ (x - 9)(x + 8) $

14. $ x^2 + 2x - 63 $
→ Multiply to $-63$, add to $2$: $9$ and $-7$
→ $ (x + 9)(x - 7) $

15. $ x^2 + 13x + 40 $
→ Multiply to $40$, add to $13$: $8$ and $5$
→ $ (x + 8)(x + 5) $

16. $ x^2 - 2x - 8 $
→ Multiply to $-8$, add to $-2$: $-4$ and $2$
→ $ (x - 4)(x + 2) $

17. $ x^2 + x - 6 $
→ Multiply to $-6$, add to $1$: $3$ and $-2$
→ $ (x + 3)(x - 2) $

18. $ x^2 - 4x + 3 $
→ Multiply to $3$, add to $-4$: $-3$ and $-1$
→ $ (x - 3)(x - 1) $

19. $ x^2 + 4x - 5 $
→ Multiply to $-5$, add to $4$: $5$ and $-1$
→ $ (x + 5)(x - 1) $

20. $ x^2 - 2x - 35 $
→ Multiply to $-35$, add to $-2$: $-7$ and $5$
→ $ (x - 7)(x + 5) $

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✔ Final Answers:

1. $ (x - 9)(x + 5) $
2. $ (x - 6)(x + 1) $
3. $ (x - 8)(x - 9) $
4. $ (x - 6)(x + 6) $
5. $ (x + 8)(x - 1) $
6. $ (x - 9)(x + 6) $
7. $ (x + 1)(x + 2) $
8. $ (x + 6)(x - 3) $
9. $ (x + 8)(x + 9) $
10. $ (x + 4)(x + 6) $
11. $ (x - 8)(x - 1) $
12. $ (x + 7)(x - 6) $
13. $ (x - 9)(x + 8) $
14. $ (x + 9)(x - 7) $
15. $ (x + 8)(x + 5) $
16. $ (x - 4)(x + 2) $
17. $ (x + 3)(x - 2) $
18. $ (x - 3)(x - 1) $
19. $ (x + 5)(x - 1) $
20. $ (x - 7)(x + 5) $

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Let me know if you'd like these checked or explained further!