Section 2.5 - Multiplying A Polynomial By A Monomial
This quiz focuses on the algebraic operation of multiplying a polynomial by a monomial, testing skills in expanding expressions and identifying missing factors or terms in polynomial equations.
- 1.
Expand 2(-c^2 + 5c - 3)
- A.
-2c^2 + 7c - 5
- B.
-c^2 + 7c - 5
- C.
-2c^2 + 10c - 6
- D.
2c^2 + 10c - 6
Correct Answer
C. -2c^2 + 10c - 6Explanation
The given expression is 2(-c^2 + 5c - 3). To expand this expression, we distribute the 2 to each term inside the parentheses. This gives us -2c^2 + 10c - 6. Therefore, the correct answer is -2c^2 + 10c - 6.Rate this question:
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- 2.
Expand -4y^2(2y^2 - 5y + 6)
- A.
8y^4 - 20y^3 + 24y^2
- B.
-8y^4 + 20y^3 - 24y^2
- C.
-8y^4 - 20y^3 - 24y^2
- D.
-8y^4 - 4y^2
Correct Answer
B. -8y^4 + 20y^3 - 24y^2Explanation
The given expression can be expanded by distributing -4y^2 to each term inside the parentheses. This results in -8y^4 + 20y^3 - 24y^2.Rate this question:
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- 3.
Expand -w(5w^2 + w - 6)
- A.
-5w^2 - w + 6
- B.
-4w^3 - 2w^2 + 6w
- C.
-5w^3 - 2w^2 + 6w
- D.
-5w^3 - w^2 + 6w
Correct Answer
D. -5w^3 - w^2 + 6wExplanation
The given expression is -w(5w^2 + w - 6). To expand this expression, we distribute the -w to each term inside the parentheses. This gives us -5w^3 - w^2 + 6w. Therefore, the correct answer is -5w^3 - w^2 + 6w.Rate this question:
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- 4.
What is the missing factor (__?__) (4x - 7) = -8x + 14
- A.
-1/2
- B.
-2
- C.
1/2
- D.
2
Correct Answer
B. -2Explanation
To find the missing factor, we need to solve the equation. We can start by distributing the factor to the terms inside the parentheses: -2(4x - 7) = -8x + 14. This simplifies to -8x + 14 = -8x + 14. Since the variables and constants are the same on both sides of the equation, this means that any value for the missing factor would satisfy the equation. Therefore, the missing factor could be any real number, including -2.Rate this question:
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- 5.
What are the missing terms in -3m(______)=12m^3 - 9m^2 + 6m
- A.
-4m^2+ 3m -2
- B.
4m^2 -3m + 2
- C.
-4m^2 -3m -2
- D.
-4m^2 + 3m -2m
Correct Answer
C. -4m^2 -3m -2Explanation
The given equation is -3m(______) = 12m^3 - 9m^2 + 6m. To find the missing terms, we need to divide both sides of the equation by -3m. This will give us the missing terms on the left side. Dividing each term on the right side by -3m, we get -4m^2 -3m -2. Therefore, the missing terms in the equation are -4m^2 -3m -2.Rate this question:
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- 6.
What are the missing terms in 2xy(_________) = 6x2y-2xy3+6x2y2
- A.
3 + 2xy^2 - 3y
- B.
-3x + y^2 - 3xy
- C.
3x + y^2 - 3xy
- D.
3x - y^2 + 3xy
Correct Answer
D. 3x - y^2 + 3xyExplanation
In order to find the missing terms, we can compare the given equation with the answer choices. We notice that the first term in the equation is 2xy, which matches with the term 3xy in the answer choice. The second term in the equation is 6x^2y, which matches with the term 3x in the answer choice. Finally, the third term in the equation is -2xy^3, which matches with the term -y^2 in the answer choice. Therefore, the missing terms in 2xy(_________) = 6x^2y - 2xy^3 + 6x^2y^2 are 3x - y^2 + 3xy.Rate this question:
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- 7.
Write a simplified algebraic expression for the area of the figure shown above
- A.
15z
- B.
-11z + 3
- C.
30z^2 + 15z
- D.
30z^2 - 15z
Correct Answer
D. 30z^2 - 15zExplanation
The given expression represents the area of the figure shown above. It is obtained by multiplying the length and width of the figure, which are represented by the terms 30z^2 and -15z respectively. Therefore, the simplified algebraic expression for the area is 30z^2 - 15z.Rate this question:
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- 8.
Write a simplified algebraic expression for the area of the figure shown above (parallelogram, Area = (b)(h) )
- A.
35n^2
- B.
25n^2 + 10n
- C.
35^2 + 14n
- D.
17n + 2
Correct Answer
B. 25n^2 + 10nExplanation
The given answer, 25n^2 + 10n, represents a simplified algebraic expression for the area of the parallelogram. It correctly combines the base and height of the parallelogram, represented by the variables n and 5n, respectively. By multiplying these two terms, we get 25n^2. Additionally, the expression includes the area of the rectangle on top of the parallelogram, which is represented by the term 10n. Therefore, the expression 25n^2 + 10n is the correct simplified algebraic expression for the area of the figure.Rate this question:
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- 9.
Write a simplified algebraic expression for the area of the figure shown above (trapezoid, Area = [(top + bottom)(height)] / 2 )
- A.
36x^2 + 9x
- B.
48x^2
- C.
28x+3
- D.
36x^2
Correct Answer
A. 36x^2 + 9xExplanation
The given expression represents the area of a trapezoid. The formula for the area of a trapezoid is [(top + bottom)(height)] / 2. In this case, the expression 36x^2 + 9x represents the area of the trapezoid. The term 36x^2 represents the product of the top and bottom lengths of the trapezoid, and the term 9x represents the height of the trapezoid. Therefore, the expression 36x^2 + 9x is the simplified algebraic expression for the area of the trapezoid.Rate this question:
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![Write a simplified algebraic expression for the area of the figure shown above (trapezoid, Area = [(top + bottom)(height)] / 2 ) - ProProfs](https://static.flickr.com/3299/3316460610_db252ba1c7_m.jpg "Write a simplified algebraic expression for the area of the figure shown above (trapezoid, Area = [(top + bottom)(height)] / 2 )")
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Aug 21, 2023Quiz Edited by
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Feb 25, 2009Quiz Created by
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