Algebra 1 Practice Test: Adding, Subtracting and Multiplying Polynomials
- Polynomial Operations
- 10 questions
- 13 minutes
These 10 questions cover combining like terms, subtracting polynomials and multiplying binomials and trinomials. When you subtract a polynomial, change the sign of every term inside the parentheses.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Simplify (3x2 + 2x − 5) + (x2 − 6x + 4).
Correct answer: C
Combine like terms: 3x2 + x2 = 4x2, 2x − 6x = −4x, and −5 + 4 = −1. Adding exponents gives the trap x4, but addition never changes exponents.
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Question 2
Simplify (5x2 − 3x + 2) − (2x2 + 4x − 7).
Correct answer: A
Change every sign in the second polynomial: 5x2 − 3x + 2 − 2x2 − 4x + 7 = 3x2 − 7x + 9. Changing only the first sign gives 3x2 + x − 5.
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Question 3
Simplify 2x(3x2 − 4x + 1).
Correct answer: D
Multiply 2x by every term: 6x3, −8x2 and 2x. Forgetting to multiply the last term leaves +1.
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Question 4
Multiply (x + 4)(x − 7).
Correct answer: B
FOIL: x2 − 7x + 4x − 28 = x2 − 3x − 28. Leaving out the middle terms gives x2 − 28.
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Question 5
Expand (2x − 3)2.
Correct answer: C
Write it as (2x − 3)(2x − 3) = 4x2 − 6x − 6x + 9. Squaring each term separately misses the middle term −12x.
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Question 6
Multiply (3x + 2)(2x − 5).
Correct answer: A
FOIL: 6x2 − 15x + 4x − 10 = 6x2 − 11x − 10. The middle terms are −15x and +4x, which combine to −11x.
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Question 7
Multiply (x − 5)(x + 5).
Correct answer: D
This is a difference of squares: the middle terms 5x and −5x cancel, leaving x2 − 25.
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Question 8
What is the degree of the polynomial 4x3 − 7x5 + x − 2?
Correct answer: B
The degree is the highest exponent of any term, which is 5 in −7x5. The first term written is not necessarily the one with the highest degree.
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Question 9
Multiply (x + 2)(x2 − 3x + 1).
Correct answer: A
Multiply each term: x3 − 3x2 + x plus 2x2 − 6x + 2. Combining gives x3 − x2 − 5x + 2. Multiplying only by x gives the second option.
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Question 10
A rectangle has length 2x + 3 and width x − 1. Which expression gives its area?
Correct answer: C
Area is length times width: 2x2 − 2x + 3x − 3 = 2x2 + x − 3. 6x + 4 is the perimeter, not the area.
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