UNIT 5
Polynomials and Properties of Exponents
LESSON 7
Polynomials and Properties of Exponents Unit Test
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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
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
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.
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Is there anything else you need help with?
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
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.
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
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.