Algebra 1 Practice Test: Exponents, Polynomials and Factoring
- Exponents, Polynomials and Factoring
- 15 questions
- 20 minutes
These 15 questions practice the laws of exponents, negative and rational exponents, scientific notation, adding, subtracting and multiplying polynomials, special products and factoring. After factoring, multiply the factors back out to check your answer.
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 (2x3y)2 · 3xy4.
Correct answer: A
(2x3y)2 = 4x6y2. Multiplying by 3xy4 gives 12x6 + 1 y2 + 4 = 12x7y6. Squaring the 3 as well gives 36, but the 3 is outside the parentheses.
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Question 2
Which expression is equivalent to x−2y3x4y−1, where x ≠ 0 and y ≠ 0?
Correct answer: A
Subtract exponents: x−2 − 4 = x−6 and y3 − (−1) = y4. So the expression is y4x6. Getting y2 comes from subtracting −1 as if it were +1.
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Question 3
What is the value of 82/3?
Correct answer: C
82/3 is the square of the cube root of 8. The cube root of 8 is 2, and 22 = 4. Multiplying 8 · 23 gives 163, which treats the exponent as a factor.
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Question 4
What is the value of 50 + 2−3?
Correct answer: D
50 = 1 and 2−3 = 123 = 18, so the sum is 98. Treating 50 as 0 gives 18, and treating 2−3 as −6 gives −5.
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Question 5
Simplify (4x2 − 3x + 7) − (x2 + 5x − 2).
Correct answer: B
Distribute the minus sign to every term: 4x2 − 3x + 7 − x2 − 5x + 2 = 3x2 − 8x + 9. Subtracting only the first term gives 3x2 + 2x + 5.
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Question 6
Which expression is equivalent to (2x − 5)(x + 3)?
Correct answer: C
2x · x + 2x · 3 − 5 · x − 5 · 3 = 2x2 + 6x − 5x − 15 = 2x2 + x − 15. Multiplying only the first and last terms gives 2x2 − 15.
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Question 7
Which expression is equivalent to (3x − 4)2?
Correct answer: D
(a − b)2 = a2 − 2ab + b2, so (3x)2 − 2(3x)(4) + 42 = 9x2 − 24x + 16. Squaring each term separately loses the middle term −24x.
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Question 8
Which is the factored form of 6x3 − 15x2 using the greatest common factor?
Correct answer: A
The GCF of the coefficients is 3 and of the variable parts is x2. Dividing each term by 3x2 leaves 2x − 5. The other forms either leave a common factor inside or do not multiply back correctly.
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Question 9
Factor x2 − 5x − 24.
Correct answer: B
You need two numbers with product −24 and sum −5: −8 and 3. (x + 8)(x − 3) would give a middle term of +5x.
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Question 10
Factor 3x2 + 10x − 8.
Correct answer: C
Check by multiplying: (3x − 2)(x + 4) = 3x2 + 12x − 2x − 8 = 3x2 + 10x − 8. (3x − 4)(x + 2) gives a middle term of 2x, and (3x + 2)(x − 4) gives −10x.
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Question 11
Factor 49x2 − 25.
Correct answer: D
This is a difference of squares: (7x)2 − 52 = (7x − 5)(7x + 5). (7x − 5)2 would include the middle term −70x.
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Question 12
Factor 2x3 − 18x completely.
Correct answer: B
First take out the GCF 2x: 2x(x2 − 9). Then x2 − 9 is a difference of squares, so the complete factorization is 2x(x − 3)(x + 3). Stopping at 2x(x2 − 9) is not complete.
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Question 13
What is (3.2 · 105)(4 · 10−2) written in scientific notation?
Correct answer: B
3.2 · 4 = 12.8 and 105 · 10−2 = 103, giving 12.8 · 103 = 1.28 · 104. In scientific notation the first factor must be at least 1 and less than 10.
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Question 14
What are the degree and leading coefficient of 5 − 2x4 + 7x3 − x?
Correct answer: C
Written in standard form the polynomial is −2x4 + 7x3 − x + 5. The highest power is 4, and its coefficient, including the sign, is −2.
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Question 15
A rectangle has length 2x + 3 and width x − 4. Which expression represents its area?
Correct answer: D
Area = (2x + 3)(x − 4) = 2x2 − 8x + 3x − 12 = 2x2 − 5x − 12. The expression 6x − 2 is the perimeter, 2(2x + 3) + 2(x − 4).
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