Question

UNIT 5
Polynomials and Properties of Exponents
LESSON 7
Polynomials and Properties of Exponents Unit Test

Answer 1

Add or subtract.
(m^2 – m – 4) + (m – 5)
A. m^2 – 2m + 9
B. m^2 + 2m – 9
C. m^2 – 2m – 9
D. m^2 – 9

Answer 2

(imposter never responded) :[

Answer 3

oh

Answer 4

Add or subtract.
(4x^2 – 2x – 1) – (–3x^3 + 2)
A. –3x^3 + 4x^2 – 2x + 1
B. –3x^3 + 4x^2 – 2x – 3
C. 3x^3 + 4x^2 – 2x + 1
D. 3x^3 + 4x^2 – 2x – 3

Answer 5

Suppose you earned 7t – 1 dollars on Monday and 8t + 5 dollars on Tuesday. What were your total earnings? Simplify your answer.
A. –t + 4 dollars
B. –t – 6 dollars
C. 15t – 6 dollars
D. 15t + 4 dollars

Answer 6

f^7 ∙ f^1
A. f^8
B. f^7
C. (2f)^8
D. (2f)^7

Answer 7

Start Fraction 100 superscript 12 baseline over 100 superscript 8 baseline End Fraction
A. 100 superscript Start Fraction 12 over 8 End Fraction baseline
B. 10096
C. 1004
D. 10020

Answer 8

Start Fraction x superscript 13 baseline over x squared End Fraction
A. x superscript thirteen-halves baseline
B. x^15
C. x^11
D. x^26

Answer 9

Which of the following expressions is true?
A. 4^3 • 4^5 < 4^12
B. 5^2 • 5^3 > 5^5
C. 3^2 • 3^4 = 3^2
D. 5^2 • 5^4 = 5^8

Answer 10

Which of the following expressions is true?
A. 8^3 • 8^2 < 8^4
B. 4^4 • 4^4 = 4^16
C. 2^2 • 2^6 < 2^8
D. 3^3 • 3^3 > 3^5

Answer 11

Write the value of the expression.
Start Fraction 4 superscript 5 baseline over 4 superscript 5 baseline End Fraction
A. 1
B. 4
C. 5
D. 0

Answer 12

Start Fraction 2 squared over 2 superscript 5 baseline End Fraction
A. 8
B. 6
C. one-eighth
D. –8

Answer 13

Multiply. Write the result in scientific notation.
(2.3 • 10^1)(7 • 10^6)
A. 1.61 • 10^7
B. 1.61 • 10^8
C. 9.3 • 10^6
D. 9.3 • 10^7

Answer 14

(1.1 ∙ 10–^5)(3 ∙ 10–^2)
A. 4.1 ∙ 10–^7
B. 4.1 ∙ 10^10
C. 3.3 ∙ 10–^7
D. 3.3 ∙ 10^10

Answer 15

Simplify the expression.
8t^5 ∙ 8t^5
A. 64t^25
B. 64t^10
C. 16t^10
D. 16t^5

Answer 16

Simplify the expression.
–x(6x – 7)
A. –6x^2 + 7x
B. 5x^2 – 6x
C. 6x + 7x
D. –6x – 7x

Answer 17

Simplify the expression.
5k^2(–6k^2 – 2k + 6)
A. –30k^3 + 3k^2 + 30k
B. 30k^4 – 10k^3 + 11k^2
C. –k^4 + 3k^3 + 11k^2
D. –30k^4 – 10k^3 + 30k^2

Answer 18

Simplify the expression.
(3k + 2)(k – 3)
A. 3k^2 – 7k – 5
B. 3k^2 – 7k – 6
C. 3k^2 – 4k – 6
D. 3k^2 – 4k – 5

Answer 19

Simplify the expression.
(–y + 4)(2y – 1)
A. 2y^2 + 7y + 3
B. 2y^2 + 5y – 4
C. –2y^2 + 9y – 4
D. –2y^2 + 6y + 3

Answer 20

Short Answer

Note: For questions 22–23, your teacher will grade your response to ensure you receive proper credit for your answer.
Look at the given triangles.
triangles

The blue triangle is a right triangle. The vertical leg is labeled with the expression 4 x plus 2. The horizontal leg is labeled with the expression 5 x minus 4. The hypotenuse is labeled with the expression 7 x plus 7.

The red triangle is a right triangle. The vertical leg is labeled with the expression x plus 3. The horizontal leg is labeled with the expression x plus 7. The hypotenuse is labeled with the expression 2 x minus 5.


a. Write an expression in simplest form for the perimeter of each triangle.

b. Write another expression in simplest form that shows the difference between the perimeter of the larger triangle and the perimeter of the smaller triangle.

c. Find the perimeter for each triangle when x = 3

Answer 21

Emma, Erin, and Eden completed the problem to the right.
a. Who completed the problem correctly?

b. What did the other two students do wrong in their answers?

Emma's equation shows 6 squared times 6 superscript 5 baseline equals 36 superscript 7 baseline.
Erin's equation shows 6 squared times 6 superscript 5 baseline equals 6 superscript 10 baseline.
Eden's equation shows 6 squared times 6 superscript 5 baseline equals 6 superscript 7 baseline.

Answer 22

Hmmmm- I see...

Answer 23

1. 6g + 8k - 9g + 2k
A. 3g + 10k
B. -2g+ 10k
C. 17gk
D. 10k - 3

Answer 24

1. 6g + 8k - 9g + 2k
A. 3g + 10k
B. -3g+ 10k
C. 17gk
D. 10k - 3

Answer 25

1. What is the degree of the polynomial 3x^4 + 2x^2 - x + 6 ?
a. 4
b. 2
c. 1
d. 3

Answer: a. 4

2. Simplify the expression 5x^3 * 2x^4.
a. 7x^7
b. 10x^7
c. 10x^12
d. 7x^12

Answer: c. 10x^12

3. Which of the following is equivalent to (2x - 3)^2 ?
a. 4x^2 - 6x + 9
b. 4x^2 - 12x + 9
c. 4x^2 - 6x - 9
d. 4x^2 - 12x - 9

Answer: a. 4x^2 - 6x + 9

4. Find the product of (3x - 2) and (x + 4).
a. 3x^2 + 12x - 2x - 8
b. 3x^2 - 2x + 12x - 8
c. 3x^2 + 4x - 8
d. 3x^2 + 4x + 8

Answer: d. 3x^2 + 4x + 8

5. What is the sum of the cubes of the roots of the polynomial x^3 - 8x^2 + 3x - 10?
a. -125
b. -153
c. -243
d. -269

Answer: c. -243

Answer 26

The solution is:

(m^2 – m – 4) + (m – 5) = m^2 + (-m + m) + (-4 - 5)
Simplifying and combining like terms, we get:
= m^2 - 9

Therefore, the answer is D. m^2 - 9.

Answer 27

Is there anything else you need help with?

Answer 28

The solution is:

(4x^2 – 2x – 1) – (–3x^3 + 2) = 4x^2 – 2x – 1 + 3x^3 – 2
Simplifying and combining like terms, we get:
= 3x^3 + 4x^2 - 2x - 3

Therefore, the answer is D. 3x^3 + 4x^2 - 2x - 3.

Answer 29

The solution is:

Total earnings = earnings on Monday + earnings on Tuesday

= (7t - 1) + (8t + 5)

= 7t + 8t - 1 + 5

Simplifying and combining like terms, we get:

= 15t + 4

Therefore, the answer is D. 15t + 4 dollars.

Answer 30

The solution is:

f^7 ∙ f^1 = f^(7 + 1) = f^8

Therefore, the answer is A. f^8.

Answer 31

The solution is:

100^12/100^8 = 100^(12-8) = 100^4

Therefore, the answer is C. 1004.

Answer 32

The solution is:

x^13/x^2 = x^(13-2) = x^11

Therefore, the answer is C. x^11.

Answer 33

The solution is:

Using the properties of exponents,

A. 4^3 • 4^5 = 4^8 and 4^8 < 4^12, so expression A is true.

B. 5^2 • 5^3 = 5^5 and 5^5 is not greater than 5^5, so expression B is false.

C. 3^2 • 3^4 = 3^6 and 3^2 is not equal to 3^6, so expression C is false.

D. 5^2 • 5^4 = 5^6 and 5^6 is not equal to 5^8, so expression D is false.

Therefore, the answer is A. 4^3 • 4^5 < 4^12.

Answer 34

The solution is:

Using the properties of exponents,

A. 8^3 • 8^2 = 8^5 and 8^5 is not less than 8^4, so expression A is false.

B. 4^4 • 4^4 = 4^8 and 4^8 is not equal to 4^16, so expression B is false.

C. 2^2 • 2^6 = 2^8 and 2^8 is equal to 2^8, so expression C is true.

D. 3^3 • 3^3 = 3^6 and 3^6 is not greater than 3^5, so expression D is false.

Therefore, the answer is C. 2^2 • 2^6 < 2^8.

Answer 35

The solution is:

4^5/4^5 = 1

Therefore, the answer is A. 1.

Answer 36

The solution is:

2^2/2^5 = 1/2^3 = 1/8

Therefore, the answer is C. one-eighth.

Answer 37

The solution is:

(2.3 • 10^1)(7 • 10^6) = (2.3 * 7) * 10^(1+6) = 16.1 * 10^7

Expressing this in scientific notation format, we get:

= 1.61 * 10^8

Therefore, the answer is B. 1.61 * 10^8.

Answer 38

The solution is:

(1.1 ∙ 10^–5)(3 ∙ 10^–2) = (1.1 * 3) * 10^(-5 - 2) = 3.3 * 10^(-7)

Expressing this in scientific notation format, we get:

= 3.3 ∙ 10–^7

Therefore, the answer is C. 3.3 ∙ 10–^7.

Answer 39

The solution is:

8t^5 ∙ 8t^5 = (8 ∙ 8) * t^(5 + 5) = 64t^10

Therefore, the answer is B. 64t^10.

Answer 40

The solution is:

-x(6x – 7) = -6x^2 + 7x

Therefore, the answer is A. –6x^2 + 7x.

Answer 41

The solution is:

5k^2(–6k^2 – 2k + 6) = -30k^4 - 10k^3 + 30k^2

Therefore, the answer is D. –30k^4 – 10k^3 + 30k^2.

Answer 42

The solution is:

(3k + 2)(k – 3) = 3k^2 -9k + 2k - 6

Simplifying and combining like terms, we get:

= 3k^2 - 7k - 6

Therefore, the answer is B. 3k^2 - 7k - 6.

Answer 43

The solution is:

(–y + 4)(2y – 1) = -2y^2 + y + 8y - 4

Simplifying and combining like terms, we get:

= -2y^2 + 9y - 4

Therefore, the answer is C. –2y^2 + 9y – 4.

Answer 44

a. The expression for the perimeter of the blue triangle is:

Perimeter = (4x + 2) + (5x - 4) + (7x + 7) = 16x + 5

The expression for the perimeter of the red triangle is:

Perimeter = (x + 3) + (x + 7) + (2x - 5) = 4x + 5

b. The difference between the perimeter of the larger triangle (blue triangle) and the perimeter of the smaller triangle (red triangle) is:

(16x + 5) - (4x + 5) = 12x

So, the expression for the difference is: 12x

c. When x = 3, we can substitute the value of x in the expressions we obtained in part (a) to find the perimeter of each triangle:

Perimeter of blue triangle = 16x + 5 = 16(3) + 5 = 53

Perimeter of red triangle = 4x + 5 = 4(3) + 5 = 17

Therefore, the perimeter of the blue triangle is 53 units and the perimeter of the red triangle is 17 units when x = 3.

Answer 45

a. Emma completed the problem correctly.

b. Erin multiplied 6^2 and 6^5 incorrectly. Instead of adding the exponents, she multiplied them and got 6^10, which is incorrect.

Eden also made a mistake in multiplying 6^2 and 6^5. Instead of adding the exponents, she just multiplied them and got 6^7, which is incorrect.

Answer 46

Please let me know if you have any questions or need further clarification on the problem.

Answer 47

6g + 8k - 9g + 2k = (6g - 9g) + (8k + 2k) = -3g + 10k

Therefore, the answer is B. -2g + 10k.

Answer 48

Correcting my previous response:

6g + 8k - 9g + 2k = (6g - 9g) + (8k + 2k) = -3g + 10k

Therefore, the answer is B. -3g+ 10k.