Part 9

15. p^3 + 7p^2 + 14p + 8.

16. 18a^2 b + 60ab^2 + 50b^3.

17. x^3 - 7x + 6.

18. 24c^2 d^2 - 47cd - 75.

19. (a^2 - b^2)^2 - (a^2 - ab)^2.

20. a^2 x^3 - (8a^2)/(y^3) - x^3 + 8/(y^3).

21. gt - gk + gl^2 + xt - xk + xl^2.

22. (m - n)(2a^2 - 2ab) + (n - m)(2ab - 2b^2).

23. a^2 - x^2 - y^2 + b^2 + 2ab + 2xy.

24. (2c^2 + 3d^2)a + (2a^2 + 3c^2)d.

25. (n(n - 1))/(1 . 2) a^(n - 2) b^2 + (n(n - 1)(n - 2))/(1 . 2 . 3) a^(n - 3) b^3.

26. (x - x^2)^3 + (x^2 - 1)^3 + (1 - x)^3. (M. I. T.)

27. (27y^3)^2 - 2(27y^3)(8b^3) + (8b^3)^2. (Princeton.)

28. (a^3 + 8b^3)(a + b) - 6ab(a^2 - 2ab + 4b^2). (M. I. T.)

Solve by factoring:

29. x^3 = x.

30. z^2 - 4z - 45 = 0.

31. x^3 - x^2 = 4x - 4.

~Reference:~ The chapter on Factoring in any algebra.

HIGHEST COMMON FACTOR AND LOWEST COMMON MULTIPLE

Define H. C. F. and L. C. M.

Find by factoring the H. C. F. and L. C. M.:

1. 3x^2 - 3x, 12x^2 (x^2 - 1), 18x^3 (x^3 - 1).

2. (x^2 - 1)(x^2 + 5x + 6), (x^2 + 3x)(x^2 - x - 6). (Harvard.)

3. x^2 - y^2, x^2 + y^2, x^3 + y^3, x^6 + y^6, x^6 - y^6. (College Entrance Board.)

4. x^3 + x^2 - 2, x^3 + 2x^2 - 3. (Cornell.)

5. x^5 - 2x^4 + x^2, 2x^4 - 4x^3 - 4x + 6. (Yale.)

6. x^2 + a^2 - b^2 + 2ax, x^2 - a^2 + b^2 + 2bx, x^2 - a^2 - b^2 - 2ab. (Harvard.)