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Let's go through the factoring of the polynomials step by step. I'll factor each expression from the list:

### Left Column
1. \( n^2 + n - 12 \)
   \[
   (n + 4)(n - 3)
   \]

3. \( p^2 + 5p - 36 \)
   \[
   (p + 9)(p - 4)
   \]

5. \( x^2 - 2x - 3 \)
   \[
   (x - 3)(x + 1)
   \]

7. \( n^2 + 2n - 24 \)
   \[
   (n + 6)(n - 4)
   \]

9. \( p^2 - 7p + 12 \)
   \[
   (p - 3)(p - 4)
   \]

11. \( 10x^2 + 32x - 90 \)
   \[
   2(5x^2 + 16x - 45) = 2(5x - 3)(x + 3)
   \]

13. \( 5n^2 + 34n + 45 \)
   \[
   (5n + 9)(n + 5)
   \]

15. \( 7x^2 + 31x + 30 \)
   \[
   (7x + 6)(x + 5)
   \]

17. \( 2n^2 + 3n - 3 \)
   \[
   (2n - 1)(n + 3)
   \]

19. \( 7x^2 + 69x + 54 \)
   \[
   (7x + 6)(x + 9)
   \]

### Right Column
2. \( x^2 - 9x + 18 \)
   \[
   (x - 3)(x - 6)
   \]

4. \( r^2 + 4r + 3 \)
   \[
   (r + 1)(r + 3)
   \]

6. \( x^2 + 8x - 20 \)
   \[
   (x + 10)(x - 2)
   \]

8. \( v^2 + 2v - 80 \)
   \[
   (v + 10)(v - 8)
   \]

10. \( n^2 - 6n + 9 \)
   \[
   (n - 3)^2
   \]

12. \( 3a^2 - 13a - 56 \)
   \[
   (3a + 7)(a - 8)
   \]

14. \( 3n^2 - 19n - 14 \)
   \[
   (3n + 2)(n - 7)
   \]

16. \( 7x^3 + 75x^2 + 50x \)
   \[
   x(7x^2 + 75x + 50) = x(7x + 10)(x + 5)
   \]

18. \( 2m^2 + 17m - 30 \)
   \[
   (2m - 3)(m + 10)
   \]

20. \( 7n^2 - 4n \)
   \[
   n(7n - 4)
   \]

If you'd like detailed explanations for any specific problem or have questions about these solutions, feel free to ask!

### Additional Questions:
1. How can you check if a polynomial has been factored correctly?
2. What strategies can be used to factor trinomials with large coefficients?
3. Can all quadratic expressions be factored? Why or why not?
4. What is the importance of factoring in solving quadratic equations?
5. How do you factor a cubic expression like in question 16?

### Tip:
When factoring trinomials of the form \( ax^2 + bx + c \), always check if there is a greatest common factor (GCF) you can factor out first to simplify the problem.

Learn how to factor polynomials completely with this set of problems. Topics include factoring quadratic and cubic expressions, using the difference of squares, and finding the greatest common factor. Suitable for Grades 9-11.

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