Rational Exponents and Radicals
1. is equal to which of the following?
A 4 C 6
B 5 D 7
2. Does each expression equal 4 when simplified?
A Yes No
B Yes No
C Yes No
D Yes No
3. What is simplified?
4. is equal to which of the following?
A 2 C 96
B 16 D 512
5. Simplify .
6. Which expression is equivalent to b-e?
A C
B D
7. What is simplified?
8. Rewrite the expression with an exponent.
9. Rewrite the equation with an exponent that makes it true.
10. Simplify the expression
11. Simplify the expression:
12. The interest Mallory’s savings account earned can be found using the formula where p is the original amount in the account. If the original amount was $2750, what is her current balance?
Adding and Subtracting Polynomials
1. Solve What is the value
of x?
2. What is 3(5x2 - 9x) evaluated for x = -3?
3. For the expression 4xy 2z, determine if each statement is True or False.
A The expression is a monomial.
True False
B The expression has a degree of 2.
True False
C The expression has a coefficient of 4.
True False
4. What is the degree of 5x3 + 2x2y3z?
5. Is each of the following a cubic binomial?
A 2x3 + 4x Yes No
B 3x2 + x Yes No
C x3 + 2 Yes No
D x4 + 3x2 - 11 Yes No
6. Which of the following is the correct classification of 3x3y2 - 9x + 1?
A binomial with a degree of 3
B binomial with a degree of 2
C trinomial with a degree of 3
D trinomial with a degree of 5
7. Simplify 5mn2 - 8m + mn2.
8. Find the sum of (4x3 + 2x) and
(8x3 - 5x + 4).
9. What is (2x2 - 5x - 7) - (7x2 + 3) simplified?
10. A rectangle has width w and its length is 2 units shorter than 3 times the width. Which polynomial represents the perimeter of the rectangle?
A 8w - 2
B 3w2 - 2w - 4
C
D 8w - 4
11. The amount Tomas makes, in dollars, working h hours can be represented by the expression 18h + 8. Tomas hopes to get a raise that can be represented by the expression 2h + 32. Write an expression that represents how much Tomas will make working h hours if he gets the raise. How much will he make for working 8 hours?
12. Graph
13. Identify each expression as a monomial, polynomial, or neither. Classify each polynomial by its number of terms and degree.
a. 9x4
b.
c.
14. Write in standard form.
15. Simplify: (4x2 + 21xy - 7y2) +
(10x2 + 11y2 - 20).
16. The area of three sections of a composite figure are labeled on the figure below.
a. Write a polynomial in simplest terms that represents the area of the figure modeled above.
b. Find the area of the figure if m.
17. Find the opposite of 7x2 - 5x by simplifying -1(7x2 - 5x).
18. Simplify:
(32mn2 + 50m2n) - (10mn2 - 16m2n + 64).
19. A company’s cost, in dollars, of making x tablet computers can be represented by . The predicted revenue of selling x tablet computers is dollars. Write a polynomial that represents the profit of selling x computers. If the company sells 150 computers, will it make a profit? If so, how much? Explain your answer.
Multiplying Polynomials
1. Find the product of and .
______
2. Find the product of 8xy and 3x - 7y.
3. What is the product of (3x + 1)(3x - 4)?
4.
a. Write a polynomial to find the volume of the rectangular prism.
b. Find the volume if feet.
5. Multiply 3x3 - x2 + 4 by x - 5.
6. Simplify (rs3 - 12) (rs3 + 12).
7. Multiply
8. Multiply .
9. Which product results in x2 - 100?
A (x - 10)2
B (x + 10)2
C x(x - 100)
D (x + 10)(x - 10)
10. Is each of the following a perfect square trinomial?
A x2 + 10x + 25 Yes No
B x2 + 16x + 16 Yes No
C x2 + 7x + 49 Yes No
D x2 + 50x + 625 Yes No
11. Multiply (x - 1) (3x2 + 6x -12).
12. The area of a carpet is 36x2y - 9xy square inches. If the width is 3xy inches, what is the length of the carpet?
13. Multiply (x - 4)2.