Expert: Richard J. Raridon - 1/5/2012

Question
1. Simplify, arrange the terms in order of decreasing degree of x and find the degree of the polynomial for:

2x3 - 7 + 5x2 - x3 + 3x - x3

2. Simplify, arrange the terms in order of decreasing degree of x and find the degree of the polynomial for:

 7xy2z3 - 4xy2z3 + 2x2yz2 - 3xy2z3

3. Add:

 2n2-n + 5 and n2 + 1

4. Subtract:

 4a2 + 3ab - b2 - (b2 - 2ab)

5. Simplify:

5(2n2 - 3) - 2(5n2 + 2) - 6

6. Simplify:

4[2a(3a - b) + 3ab)] + 5[3b(a + 2b) - 4ab]

7. Find an equation of the form f(x) = mx + b:

f(0) = 5 and f(2) = 7

8. Find the line (written in standard form) containing the points:

(0,0) and (-3,2)

9. Find the line (written in standard form) containing the points:

(-4,7) and (1,9)

10. Simplify (assume the variable represents positive integers):

(-t3)4

11. Simplify (assume the variables represent positive integers):

(r2s)(-3rs2)(2rs)

12. Simplify (assume the variables represent positive integers):

(2x2y3)3(3x3y)2

13. Simplify (assume the variable exponents represent positive integers):

(yp+2)(yp)(yp-2)

14. Simplify (assume the variable exponents represent positive integers):

x2(xk - xk-1 + xk-2)

15. Simplify:

(2x - 3)(3x + 2)

16. Simplify:

(r - 4)(3r - 2)

17. Simplify:

(4k - 5)2

18. Simplify:

(2s + 7)(2s - 7)

19. Simplify:

(9 - 5t)(5t - 9)

20. Simplify:

(p2 - 2q2)(p2 + 2q2)

21. Simplify:

(2z2 - 5)2

22. Simplify:

x2(x - 3)(x + 3)

23. Simplify:

(t - 3)(2t2 - t + 2)

24. Simplify:

(3 - k2)(2 - k2 - k4)

25. Simplify:

(y2 - 2y + 1)(y2 + y +1)

26. Simplify:

(x2n - yn)2

27. Simplify:

(xn + 1)(xn - 1)

28. Simplify:

(a + b)2

29. Simplify:

(a - b)(a2 + ab + b2)

30. Simplify:

(x2 - 4x + 8)(x2 + 4x + 8)

31. Provide the prime factorization for the integer: 756

32. Provide the prime factorization for the integer: 3,861

33. Find the GCF and LCM for the monomials: 30, 35, 36, 42

34. Find the GCF and LCM for the monomials: 52r2s, 78rs2t

35. Find the GCF and LCM for the monomials: 22xy2z2, 33x2yz2, 44x2yz

36. A positive integer is perfect if it is the sum of all its positive factors except itself.  There are two perfect integers less than 30.  What are they?

Answer
1. 5x^2+3x-7
2. 2x^2yz^2
3. 3n^2-n+5
4. 4a^2+5ab
5. -25
6. 24a^2-ab+30b^2
7. f(x)=x+5
8. y = (-2/3)x
9. y = (2/5)x+43/5
10. t^12
11. -6r^4s^4
12. 72x^12y^4
15. 6x^2-5x-6
16. 3r^2-14r+8
17. 16k^2-40k+25
18. 4s^2-49
19. -25t^2+90t-81
20. p^4-4q^4
21. 4z^4-20z^2+25
22. x^4-9x^2
23. 2t^3-7t^2+5t-6
24. 6--5k^2-2k^4+k^6
25. y^4-y^3-y+1
26. x^4n -2x^2ny^n +y^2n
27. x^2n -1
28. a^2+2ab+b^2
29. a^3-b^3
30. x^4+64
31. (2^2)(3^3)(7)
32. (3^3)(11)(13)
33. GCF = 1, LCM = 1260
34. GCF = 26rs, LCM = 156r^2s^2t
35. GCF = 11xyz, LCM = 132x^2y^2z^2
36. 6 and 28