Expert: Richard J. Raridon - 11/1/2010

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

5x2 + 3x - 7;  degree = 2  3x3 + 5x2 + 3x - 7;  degree = 4
5x2 + 3x - 7;  degree = 6  3x3 - 5x2 + 3x - 7;  degree = 6

2. Simplify, arrange the terms in order of decreasing degree of x and find the degree of the polynomial for:
 7xy2z3 - 4xy2z3 + 2x2yz2 - 3xy2z3

14xy2z3 + 2x2yz2;  degree = 11  2x2yz2;  degree = 5
7xy2z3 + 2x2yz3;  degree = 12  2xy2z3;  degree = 4

3. Add:
 2n2-n + 5 and n2 + 1

2n2-n + 6  3n2 + n + 4
3n2 - n + 6  3n2 + 6

4. Subtract:
 4a2 + 3ab - b2 - (b2 - 2ab)

4a2 + 5ab - 2b2  4a2 + 5ab
4a2 + ab - 2b2  4a2 - 5ab - 2b2

5. Simplify:
5(2n2 - 3) - 2(5n2 + 2) - 6

100n2 - 25  20n2 - 5
20n2 - 25  -25

6. Simplify:
4[2a(3a - b) + 3ab)] + 5[3b(a + 2b) - 4ab]

24a2 - ab + 30b2  24a2 + 15ab + 30b2
24a2 + 5ab + 30b2  24a2 - 9ab + 30b2

7. Find an equation of the form f(x) = mx + b:
f(0) = 5 and f(2) = 7

f(x) = x - 5  f(x) = -x + 5
f(x) = -x - 5  f(x) = x + 5

8. Find the line (written in standard form) containing the points:
(0,0) and (-3,2)

2x + 3y = 0  y =    2 x + 1
3


x + y =    2
3

 2x - 3y = 0

9. Find the line (written in standard form) containing the points:
(-4,7) and (1,9)

5y = 2x - 47  2x - 5y = -43
y = 3x - 42  5x - 2y = 43

10. Simplify (assume the variable represents positive integers):
(-t3)4

t7  -t7
t12  -t12

11. Simplify (assume the variables represent positive integers):
(r2s)(-3rs2)(2rs)

-6r4s4  -r4s5
-6r2s3  6r3s3

12. Simplify (assume the variables represent positive integers):
(2x2y3)3(3x3y)2

6x12y11  72x12y11
6x10y11  5x10y8

13. Simplify (assume the variable exponents represent positive integers):
(yp+2)(yp)(yp-2)

y3p  yp3
y3p-5  y3p

14. Simplify (assume the variable exponents represent positive integers):
x2(xk - xk-1 + xk-2)

x2k - x2k-2 + x2k-4  2xk+2 - 2xk+1 + xk
xk+2 - xk+1 + xk  -x3k+3

15. Simplify:
(2x - 3)(3x + 2)

5x2 - 5x - 6  6x2 + 10x + 6
6x2 - 5x - 6  -36x2

16. Simplify:
(r - 4)(3r - 2)

3r2 - 12r - 8  3r2 + 14r + 8
3r2 - 14r + 8  24r2

17. Simplify:
(4k - 5)2

8k2 - 40k - 25  16k2 - 40k + 25
8k2 + 25  8k2 - 25

18. Simplify:
(2s + 7)(2s - 7)

4s2 - 28s + 49  4s2 - 49
4s2 - 28s - 49  4s2 + 49

19. Simplify:

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

-25t2 + 90t - 81  25t2 + 90t - 81
-25t2 + 81  -25t2 - 81

20. Simplify:
(p2 - 2q2)(p2 + 2q2)

2p2 + p2q2 - 4q2  p4 + 4p2q2 - 4q4
p4 + 4q4  p4 - 4q4

21. Simplify:
(2z2 - 5)2

4z4 - 20z2 + 25  4z2 + 10z2 - 25
4z4 + 20z2 - 25  -9z4

22. Simplify:
x2(x - 3)(x + 3)

3x2 - 6x - 9x2  x4 - 9x2
x4 - 6x - 9x2  x4 - 9

23. Simplify:
(t - 3)(2t2 - t + 2)

3t3 - 7t2 + 5t - 6  2t3 - 7t2 + 5t - 6
5t2 + 5t + 6  -4t2 - t

24. Simplify:
(3 - k2)(2 - k2 - k4)

6 - k2 - k4  6 - k8
k6 - 2k4 - 5k2 + 6  k6 + 2k4 - 5k2 + 6

25. Simplify:
(y2 - 2y + 1)(y2 + y +1)

2y2 - y + 2  y4 - y + 2
y4 - y3 + y + 1  y4 - y3 - y + 1

26. Simplify:
(x2n - yn)2

x4n - y2n  2x4n - 2y2n
x4n + 2x2nyn + y2n  x4n - 2x2nyn + y2n

27. Simplify:
(xn + 1)(xn - 1)

2xn  x2n + 2xn - 1
x2n - 1  x2n - 2xn - 1

28. Simplify:
(a + b)2

a3 + b3  a2 + 2ab + b2
3a3 + 3b3  a3 + 2ab2 + b2

29. Simplify:
(a - b)(a2 + ab + b2)

(a - b)2  a3 - b3
(a + b)2  a3 + b3

30. Simplify:
(x2 - 4x + 8)(x2 + 4x + 8)

(x - 6)2(x + 4)(x - 4)  (x - 6)2(x + 4)(x - 4)
x4 - 64  x4 + 64

Part 2
Short Answer: Type the answer to the problem in the text box below each item. Be sure legibly show all work in your notebook. Remember to include any applicable units. If there is no solution, type "no solution". If there is not enough information present to solve the problem, type "not enough information". (Each question is worth one point)
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
Your problems would be a lot easier to read if you learned to write exponents correctly.
1. 5x^2+3x-7, deg = 2
2. 2x^2yz^2, deg = 5
3. 3n^2-n+6
4. 4a^2+5ab-2b^2
5. -25
6. 24a^2-ab+30b^2
7. f(x) = x+5
8. 2x+3y = 0
9. 2x-5y = -43
10. t^12
11. -6r^4s^4
12. 72x^12y^11
13. y^3p
14. x^2k -x^2k-2 +x^2k-4
15. 6x^2-5x-6
16. 3r^2-14r+8
17. 16k^2-40k+25
18. 4s^2-49
19. -25t^2+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. k^6-2k^4-5k^2+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^2+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. one is 6
35.