Multiply and Simplify. Assume all variables represent nonzero numbers.
1)
=
Identify the degree of each term of the polynomial and the degree of the polynomial.
2)
What is the degree of the first term? 3
What is the degree of the second term? 2
What is the degree of the third term? 1
What is the degree of the fourth term? 0
What is the degree of the polynomial? 3
Perform the indicated operations and simplify.
3)
Use rational exponents to simplify.
4)
= x2
5) Television sets. What does it mean to refer to a 20-in TV set or a 25-in TV set? Such
units refer to the diagonal screen. A 15-in TV set has a width of 12 inches. What is its
height? 9
6) Add. Simplify your answer.
= r5 – 3r4 + 4r3 + 12r2 + 5r - 9
Solve. Choose from the 3 answers below and if necessary finish the solution provided in
the answer key.
7)
The solution is
a) {x| -3 < x < -2 or x > 19}
b) The solution is all real numbers.
c) There is no solution,
Find a polynomial for the perimeter and for the area of the square.
8) Length= a+7
Width=a
Perimeter = 4a + 14
Area = a2 + 7a
Factor completely.
9)
= (5a - 3)(5a + 3)
In a right triangle, find the side that is not given.
a=3
10) b=2
Factor the trinomial completely.
11)
= c(c - 8)(c + 6)
Subtract. Simplify by collecting like radical terms if possible.
12)
=
Simplify by factoring. Assume that all expressions under radicals represent nonnegative
numbers.
13)
=
Find the greatest common factor for the group of terms.
-5a2
14)
Factor completely.
15)
= (3w - 5)2
Add. Simplify if possible.
16)
=
Add.
17)
= -3x2 - 7xy - 4y2
For the following equation, state the value of the discriminant and then describe the
nature of the solutions from the following statements.
18)
What is the value of the discriminant? -24
Which one of the statements is true?
a) The equation has two real solutions.
b) The equation has one real solution.
c) The equation has two imaginary solutions.
Factor.
19)
= (s - 6)(s - 4)
Divide and simplify.
20)
=
Multiply and simplify by factoring. Assume that all expressions under radicals
represent nonnegative numbers.
21)
=
Solve.
22)
x=
Factor completely.
23)
= 7(4v + 7t)2
Find the vertex, the line symmetry, the maximum or minimum value of the quadratic
equation and graph the function. (Just tell me if it opens up or down and in what
direction)
24)
The x-coordinate of the vertex is?
The y-coordinate of the vertex is?
The equation of line symmetry is x =
The maximum/minimum value of f(x) is
The value
is minimum or maximum? Maximum
Does the graph open upward or downward? Downward
Find the variation constant and an equation of variation where y varies directly as x
and y=54 when x=6.
25) The variation constant is k = 9
The equation of variation is y = 9x
Subtract. Simplify is possible.
26)
Factor.
27)
=
= (r - 9)2
Use the FOIL method to find the product.
28)
= 4x14 – 3x8 – 16x6 + 12
29) a) Solve
(what are the solutions?) x =
b) Find the x-intercepts of
Use rational exponents to write
the best answer below.
30)
as a single radical expression. Choose
a)
b)
c)
d)
Simplify.
31)
=
Subtract the polynomials.
= -12s2 + 9s
32)
Evaluate the polynomial for x= -3. Simplify your answer.
33)
=
When x= -3,
= 51
Simplify by taking roots of the numerator and the denominator. Assume that all
expressions under radicals represent positive numbers.
34)
=
Solve.
35)
Express by using a positive exponent.
36)
=
Find the x-intercepts for the graph of the equation
37) The x-intercepts are: (-1, 0), (5, 0)
.
Write a quadratic equation in the variable x having the given numbers as solutions.
Type the equation in standard form
.
2
38) Solution 1, only solution. x – 2x + 1 = 0
Multiply and Simplify.
39)
=
Multiply.
= -228
40)
Find the following.
=3
41)
42) Jack usually mows his lawn in 5 hours. Marilyn can mow the same yard in 6
hours. How much time would it take for them to mow the lawn together?
Find all the numbers in which the rational expression is undefined.
43)
-5, 5
Multiply.
44)
=
Simplify by removing factors of 1.
45)
=
Factor completely.
46)
= 8x4 (x2 – 2x + 2)
Divide. Choose the correct answer.
47)
a)
b)
c)
d)
Solve.
48)
, r = -7, 6
Find the following. Assume that variables can represent any real number.
49)
= |a + 7|
50)
If a pro basketball player has a vertical leap of about 25 inches, what is his
hang time? Use the hang-time function
. 0.7
Solve.
51)
r = -2, 7
Divide and simplify.
52)
=
Multiply.
= r3 + p 3
53)
Solve.
54)
x=
Simplify by removing factors of 1.
55)
=
Rewrite the following expression with positive exponents.
56)
=
Use the quadratic formula to solve the equation.
57)
,x=
Multiply.
58)
= 64m6
Find the vertex, line symmetry, and the minimum/maximum value of f(x).
59)
What is the vertex? (-8, 3)
What is the line symmetry? (x = -8)
What is the minimum/maximum value of f(x)? 3
Is the value f(-8)=3 minimum or maximum? minimum
Does the graph open upward or downward? Upward
Solve for x.
60)
, x = -3, -1
Rewrite with a rational exponent.
61)
= 211/4
62) If the sides of a square are lengthened by 6 cm, the area becomes
the length of the side of the original square. 5
. Find
Solve.
,x=7
63)
Rationalize the denominator. Assume that all expressions under radicals represent
positive numbers.
64)
=
Multiply.
65)
= 18x3 + 57x2 + 110x + 56
Convert to decimal notation.
66)
= 83800000