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Are you looking for an algebra polynomials practice test? There are a lot of people who have a hard time when it comes to solving math problems, but one of the first steps that one should do is ensure that they first equate the equation to zero then join in like variables. Do take the quiz below and get some practice.
Questions and Answers
1.
(-x^{3} + 3x^{2} + 3) + (3x^{2} + x + 4)
A. -x^{3} + 6x^{2} + x + 7 B. -x^{3} + 9x^{2} + x + 7 C. 2x^{6} + x + 7 D. 2x^{5} - x + 7
A.
A
B.
B
C.
C
D.
D
Correct Answer A. A
Explanation The given expression is a sum of two polynomials. To simplify the expression, we combine like terms by adding the coefficients of the same degree terms. In this case, the x^3 term does not have a like term, so it remains as -x^3. The x^2 terms have a like term in each polynomial, so we add the coefficients: 3x^2 + 3x^2 = 6x^2. The x term also has a like term in each polynomial, so we add the coefficients: x + x = 2x. Finally, the constant terms have a like term in each polynomial, so we add the coefficients: 3 + 4 = 7. Therefore, the simplified expression is -x^3 + 6x^2 + 2x + 7, which matches option A.
Explanation The given expression is a sum of two polynomials. To simplify, we combine like terms by adding the coefficients of the same degree. In the first polynomial, we have -2x^3 and in the second polynomial, we have 0x^3 (since there is no x^3 term). Therefore, the x^3 term remains the same in the simplified expression. Similarly, we add the coefficients of x^2, x, and constants. The simplified expression becomes -2x^3 + 6x^2 + 6x + 9. This matches option C.
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3.
(2x^{7} + 5x + 4) + (5x^{9} + 8x)
A. 5x^{9} + 2x^{7} + 13x + 4
B. 5x^{9} + 7x^{7} + 13x + 4
C. 7x^{9} + 13x + 4 D. 7x^{16} + 13x + 4
A.
A
B.
B
C.
C
D.
D
Correct Answer A. A
Explanation The given expression is a combination of two separate terms. To simplify the expression, we can combine like terms by adding the coefficients of the same variables. In the first term, we have 2x7 and in the second term, we have 5x9. So, the correct answer is A, which rearranges the terms in ascending order of the variables and combines the coefficients of the like terms.
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4.
(3x^{6} + 4x + 3) + (3x^{8} + 6x)
A. 6x^{14} + 4x + 3
B. 3x^{8} + 10x^{7} + 13x + 4
C. 3x^{8} + 3x^{6} + 10x + 3 D. 3x^{8} + x^{6} + 4x + 3
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
Explanation The given expression is a sum of two polynomial expressions. To simplify, we can combine like terms by adding the coefficients of the same degree variables. In the first term, we have 3x^6 and in the second term, we have 3x^8. Combining these two terms, we get 3x^8 + 3x^6. Similarly, the coefficients of x terms can be combined. In the first term, we have 4x and in the second term, we have 6x. Combining these two terms, we get 10x. Finally, we have a constant term of 3 in both terms, so it remains the same. Therefore, the simplified expression is 3x^8 + 3x^6 + 10x + 3, which matches option C.
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5.
(10x^{2} + 3x + 5) + (2x^{3} + 6x + 5)
A. 12x^{5} + 3x + 10
B. 10x^{3} + 2x^{2} + 10
C. 2x^{3} + 10x^{2} + 9x + 10 D. 2x^{3} + 12x^{2} + 9x + 10
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
Explanation The given expression is a sum of two polynomials. To simplify the expression, we can add the coefficients of like terms. In the first term, 10x^2 is added to 2x^3, resulting in 12x^2. In the second term, 3x is added to 6x, resulting in 9x. Finally, the constants 5 and 5 are added, resulting in 10. Therefore, the correct answer is C: 2x^3 + 10x^2 + 9x + 10.
Explanation The given expression can be simplified by combining like terms. The terms 8x8 and 8x7 cannot be combined with any other terms since they have different variables. The term 9 can be combined with the constant terms -5 and -2x. Therefore, the correct answer is B, 8x8 + 5x7 - 2x + 4.
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7.
(9x^{8} + 8x^{7} + 9) - (6x^{7} + 2x + 2)
A. 9x^{15} + 3x^{7} + 7
B. 3x^{8} + 2x^{7}- 2x + 7
C. 9x^{8} + 2x^{7} - 2x + 7 D. 11x^{8} + 10x^{7} + 7
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
Explanation The given expression is simplified by multiplying the terms within the parentheses first and then subtracting the second set of terms from the first set. The correct answer, option C, shows the correct multiplication and subtraction of the terms.
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8.
(2x^{7} + 7x^{4} + 6) - (2x^{4} - x)
A. 2x^{7} + 9x^{4} - x + 6
B. 4x^{11} + 6x^{3} +6
C. 2x^{7} + 5x^{4} + x + 6 D. 6x^{3} + 6
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
Explanation The given expression involves addition and subtraction of terms with variables. To simplify the expression, we first perform the multiplications within the parentheses: 2x7 = 14, 7x4 = 28, and 2x4 = 8. Then, we perform the subtractions within the parentheses: 8 - x. Finally, we combine all the terms: 14 + 28 + 6 - (8 - x) = 48 - 8 + x = 40 + x. Therefore, the correct answer is C, which is 2x7 + 5x4 + x + 6.
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9.
(3x^{7} + 8x^{4} + 7) - (x^{4} - 2x)
A. 7x^{4} - x + 7x
B. 3x^{11} + 7x^{3} + 5x
C. 3x^{7} + 7x^{4} + 2x + 7 D. 2x^{7} + 6x^{3} + 6
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
Explanation The expression (3x7 + 8x4 + 7) - (x4 - 2x) simplifies to 3x7 + 7x4 + 2x + 7. Therefore, the correct answer is C.
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10.
10x^{8} + 11x^{6} - 2x + 5 - (8x^{8} + 6x^{7} - 5)
A. 2x^{0} + 5x^{1} - 2x
B. 2x^{8} - 6x^{7} + 11x^{6} - 2x + 10
C. 18x^{8} -17x^{7} + x^{6} - 2x + 10 D. 2x^{8} - 6x^{7} + 9x^{6} - x + 10
A.
A
B.
B
C.
C
D.
D
Correct Answer B. B
Explanation The given expression involves addition and subtraction of terms with different powers of x. By simplifying the expression, we can combine like terms and obtain the final result. The correct answer option B, 2x8 - 6x7 + 11x6 - 2x + 10, is obtained by combining the terms with the same powers of x and performing the necessary arithmetic operations.
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11.
Enter the degree of the polynomial below:
3x^{8} + 6x^{7} + 5x^{6} -7x^{5} + 9x^{3}
Correct Answer 8
Explanation The degree of a polynomial is determined by the highest power of the variable. In this polynomial, the highest power of x is 8, so the degree of the polynomial is 8.
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12.
Enter the degree of the polynomial below:
x^{9} + 5x^{6} + 5x^{5} + 2x^{4} - 7x^{3}
Correct Answer 9
Explanation The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the highest power of x is 9, so the degree of the polynomial is 9.
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13.
Enter the degree of the polynomial below:
6x^{7} - 8x^{6} + 4x^{5} + 10x^{4}
Correct Answer 7
Explanation The degree of a polynomial is the highest power of the variable in the expression. In this case, the highest power of x is 7, which means that the degree of the polynomial is 7.
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14.
What is the leading coefficient of the polynomial below?
4x^{9} + 6x^{7} + 5x^{5} -7x^{3} + 9
Correct Answer 4
Explanation The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this polynomial, the term with the highest degree is 4x^9. Therefore, the leading coefficient is 4.
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15.
What is the leading coefficient of the polynomial below?
11x^{8} + 2x^{4} + 3x^{3} - 8x^{2} + 4x
Correct Answer 11
Explanation The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this polynomial, the term with the highest degree is 11x^8. Therefore, the leading coefficient is 11.
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16.
What is the leading coefficient of the polynomial below?
3x^{12} + 2x^{7} + 9x^{5} - 2x^{4} + 4x^{2}
Correct Answer 3
Explanation The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this polynomial, the term with the highest degree is 3x12. Therefore, the leading coefficient is 3.
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17.
Which polynomial has the terms written in the correct order?
A. 3 + 2x^{10} + 8x^{6} + 4x^{2} - x
B. 2x^{10} + 8x^{6} + 4x^{2} - x + 3
C. 8x^{6} + 4x^{2} + 3 + 2x^{10} - x
D. 3 - x + 2x^{10} + 8x^{6} + 4x^{2}
A.
A
B.
B
C.
C
D.
D
Correct Answer B. B
Explanation The correct answer is B because it has the terms written in ascending order of their exponents. The polynomial starts with the term with the highest exponent (2x10), followed by the term with the next highest exponent (8x6), and so on. This order ensures that the terms are arranged correctly according to their powers of x.
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18.
Which polynomial has the terms written in the correct order?
A. 4 + 3x^{11} + 9x^{7} + 5x^{3} - x
B. 9x^{7} + 5x^{3} + 4 + 3x^{11} - x
C. 4 - x + 3x^{11} + 9x^{7} + 5x^{3}
D. 3x^{11} + 9x^{7} + 5x^{3} - x + 4
A.
A
B.
B
C.
C
D.
D
Correct Answer D. D
Explanation The correct answer is D because the terms are written in descending order of their exponents. The highest exponent term, 3x^11, is written first, followed by the terms with exponents in decreasing order (9x^7, 5x^3, -x, and finally 4).
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19.
Which polynomial has the terms written in the correct order?
A. 4x^{10} + 16x^{5} + 5x^{4} + x + 6
B. 16x^{5} + 5x^{4} + 6 + 4x^{10} + x
C. 6 + 5x^{4} + 4x^{10} + 16x^{5} + x
D. x + 6 + 16x^{5} + 5x^{4} + 4x^{10}
A.
A
B.
B
C.
C
D.
D
Correct Answer A. A
Explanation The correct order of the terms in a polynomial is from highest degree to lowest degree. In option A, the terms are arranged in the correct order, with the highest degree term (4x10) followed by the next highest degree term (16x5), and so on. Option B has the terms arranged in a different order, option C has the terms arranged in a different order, and option D has the terms arranged in a different order. Therefore, option A is the correct answer.
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20.
Which of the following is NOT a polynomial?
A. 5x^{2}
B. -7x^{7} - 3 + 2x^{3}
C. 5x^{2} - 2x^{ -7} + 2
D. 2 - x^{3} + 4x^{0}
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
Explanation The expression in option C is a polynomial because it is a combination of terms involving variables raised to non-negative integer powers, and it only involves addition and subtraction operations. Therefore, the correct answer is option D, as it includes a term with a negative exponent (4x^0) which violates the definition of a polynomial.
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21.
Which of the following is NOT a polynomial?
A. 3x^{4}
B. 5x^{10} - 4x^{-8} + 2
C. x^{8} + 2x^{3} + 7
D. 5 - x^{2} + 7x^{0}
A.
A
B.
B
C.
C
D.
D
Correct Answer B. B
Explanation A polynomial is an algebraic expression with one or more terms, where each term consists of a coefficient and a variable raised to a non-negative integer exponent. Option B, 5x10 - 4x-8 + 2, is not a polynomial because it has a negative exponent (-8) on the variable x.