https://file.aiquickdraw.com/mathbot/file/1725722368832t7ne66mb.jpg

The image contains two sections of problems related to factoring polynomials. I'll go over each section and guide you through the process.

### II. Complete each factorization:
These are algebraic expressions that need to be factored completely.

6. \( a^2 + 12a + 11 = (a + 1)(a + 11) \)

7. \( a^2 + 7a + 6 = (a + 1)(a + 6) \)

8. \( x^2 - 36 = (x - 6)(x + 6) \)

9. \( x^4 - 30x^2 + 144 = (x^2 - 6)(x^2 - 24) \)

10. \( y^2 - 16 = (y - 4)(y + 4) \)

11. \( r^2 - 36r + 45 = (r - 3)(r - 15) \)

### III. Factor each completely, if possible. If not, state that it's prime:

12. \( x^2 + 9x + 18 = (x + 3)(x + 6) \)

13. \( 2x^2 + 8x + 6 = 2(x + 1)(x + 3) \)

14. \( y^2 - 16 = (y - 4)(y + 4) \)

15. \( x^2 + 10x + 25 = (x + 5)(x + 5) = (x + 5)^2 \)

16. \( 3x^2 + 13x + 10 = (3x + 5)(x + 2) \)

17. \( x^2 - x - 12 = (x - 4)(x + 3) \)

18. \( x^2 - 81 = (x - 9)(x + 9) \)

19. \( 5y^2 - 20 = 5(y - 2)(y + 2) \)

20. \( z^2 + 9 = \text{Prime (does not factor over real numbers)} \)

21. \( p^2 - 5p - 36 = (p - 9)(p + 4) \)

22. \( x^2 + 10x + 16 = (x + 2)(x + 8) \)

23. \( 9a^2 - 49 = (3a - 7)(3a + 7) \)

24. \( 45 - 4z^2 = (3 + 2z)(3 - 2z) \)

25. \( 2x^2 + 14x + 20 = 2(x + 2)(x + 5) \)

26. \( z^2 + 10z + 25 = (z + 5)(z + 5) = (z + 5)^2 \)

27. \( 16a^2 - 81 = (4a - 9)(4a + 9) \)

28. \( 36y^2 - 49 = (6y - 7)(6y + 7) \)

---

Let me know if you want a detailed explanation for any specific problem or need further clarifications!

### Related Questions:
1. How do you factor quadratic expressions with different leading coefficients?
2. What is the difference between factoring perfect square trinomials and difference of squares?
3. Can you always factor a quadratic expression? Why or why not?
4. What strategies can be used to factor higher-degree polynomials?
5. How can factoring be applied to solve quadratic equations?

### Tip:
Always check if you can factor out a greatest common factor (GCF) first before applying other factoring techniques!

Complete each factorization and factor each completely, if possible, as shown in the provided image.

Learn how to complete each factorization and factor polynomials completely with solutions for problems including trinomials, difference of squares, and higher-degree polynomials. This set of problems is perfect for students in Grades 9-12 studying algebraic factorization techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation