1. Convert to decimal notation. 8.19 x 10^7
Answer: 81,900,000
2) Identify the degree of each term of the polynomial and the degree of the polynomial. 9x^3+8x^2+7x+8
The degree of the first term is = 3
The degree of the second term is = 2
The degree of the third term is = 1
The degree of the fourth term is = 0
The degree of the polynomial is = 3
3. Divide and simplify. y^7/y^12
Answer: 1/y^5
4. Add. (5b^4-2b^3+5b^2+17b-9)+(b^5+10b^3+6b^2-5b+4)+(-8b^4+b^2-7b-6)
Answer: b^5-3b^4+8b^3+12b^2+5b-11
5. Simplify by factoring. sqrt50a^2b
Answer: 5a√2𝑏
7. In a right triangle, find the lenght of the side not given.
b=2, c=sqrt29
Answer: a=5
8. Multiply and simplify by factoring. ^3sqrty^13 ^3sqrt81y^14
3
Answer:3y9 √3
9. Find all numbers for which the rational expression is undefined. t^3-8t/t^2-25
Answer: -5,5
10, Multiply and simplify. b^19xb^0
Answer: b19
11. Express using a positive exponent. b^-3
Answer:1/b3
12. Divide. (25b^3+5b^2+34b+33)/(5b+3)
Choose:
A. 5b^2+2b+8
B. 5b^2-2b-8-9/5b+3
C. 5b^2-2b+8+9/5b+3 (correct)
D. 5b+8
13. Solve. c^2-4c-45=0
Answer: -5,9
14. Perform the indicated operations and simplify.
z-1/z-7 - z+1/z+7 + z-91/z^2-49
13
Answer: 𝑧+7
15. Find the greatest common factor for the group of terms. -30a^4,5a^5
Answer:5a4
16. Solve. 5/w=7/w-1/3
Answer: w=6
17. Use the rational exponents to simplify. ^3sqrtx^6
Answer: x2
18. Solve. (x+8)(x-14)(x+1)>0 –
A. The solution set is =
B. The solution is all real numbers.
C. There is no solution.
Answer: A; solution set is {x/-8<x<-1 or x>14}
19. Multiply and simplify. 49d^2/3d^2-6d+3 x 3d-3/7d
7𝑑
Answer: 𝑑−1
20. Factor completely. 49t^2+64-112t
Answer: (7t-8)(7t-8)
21. Find the following: ^12sqrt(-66)^12
Answer: 66
22. Simplify by removing factors of 1. p^2-4/(p+2)^2
𝑝−2
Answer: 𝑝+2
23. Subtract. Simplify by collecting like radical terms if possible. 8sqrt18 - 9sqrt2
Answer: 152
24. Simplify. ^3sqrt-1/27
Answer: -1/3
25. Find the variation constant and an equation of variation where y varies directly as x and y=36
when x=9.
The variation constant is k= 4
The equation of variation is y= 4x
26. Multiply. (c+1/2)(c+1/3)
Answer: c2+(5/6)c+1/6
27. Find the x-intercepts for the graph of the equation y=x^2-3x-10.
The x-intercepts are (-2,0),(5,0)
28. Factor the trinomial. b^3-2b^2-8b
Answer: b(b-4)(b+2)
29. Solve. x^2+14x-4=0
Answer: -7+√53, -7-√53
30. Multiply (c+f)(c^2-cf+f^2)
Answer: c3+f3
31. If the sides of a square are lenghtened by 5 cm, the area becomes 81 cm^2. Find the length of
the side of the original square.
Answer: 4
32. Subtract. Simplify. 5-z/z-9 - 7z-9/9-z
6𝑧−4
Answer: 𝑧−9
33. Use the quaratic formula to solve the equation. 2x^2-5x=-7
Answer:
5+√31 i 5−√31 i
4
,
4
34. Multiply. (-4x)^2(3x^2)^2
Answer: 144x6
35. Subtract the polynomials. (-6a^2+6a+4) - (7a^2+4)
Answer: -13a2+6a
36. Add. (6x^2-7xy+y^2) + (-9x^2-4xy-y^2) + (x^2+xy-7y^2)
Answer: -2x2-10xy-7y2
37. If a pro basketball player has a vertical leap of about 20 inches, what is his hang time? Use
the hang-time function V=48T^2 His hang time is __ seconds.
Answer: 0.6
38. Find the vertex, the line of symmetry and the maximum or minimum value of f(x). --f(x)=1/3(x+8)^2+1
The vertex = (-8,1)
The line of syummetry is x =-8
What is the maximum/minimum value of f(x)= 1
Is the value, F(-8), a minimum or maximum minimum
39. Use rational exponents to write x^1/4 x y^1/3 x z^1/9 as a single radical expression.
--A ^108sqrtxyz
--B ^36sqrtxyz
--C ^36sqrtx^9y^12z^4 (correct)
--D ^36sqrt(xyz)^25
40. Factor. c^2+4c+4
Answer: (c+2)(c+2)
1.
𝑣−4
𝑣
2.
0
3.
3𝑧−1
𝑧−3
4.
5.
55/3
A; 7/4
6.
7
7.
4-25p2
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
6
8
𝑎𝑛𝑑 24
49+5𝑧
175𝑧 3
2𝑦−9
11𝑦
𝑟+3
𝑟−3
𝑦−9
𝑦+5
-6
A; 8
A; -5,-1
𝑦 2 +3𝑦−10
𝑦
129𝑏
10𝑏−50
7.5
B
18 and 24
95
28𝑧
𝑥 2 +12𝑥
𝑥 2 −36
22.
55(y-11)
23.
11𝑥 6 𝑞2
3
2
5