1.
Is 3x a polynomial?
Correct Answer
A. Yes
Explanation
A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. In this case, 3x is a polynomial because it is the product of the coefficient 3 and the variable x. It does not involve any other operations or terms, making it a simple monomial polynomial.
2.
Is 5xy^{-2} a polynomial?
Correct Answer
A. No
Explanation
A polynomial is an algebraic expression with one or more terms, where each term consists of a variable raised to a non-negative integer power, multiplied by a constant coefficient. In the given expression 5xy-2, the term "5xy" is a polynomial because it consists of variables (x and y) raised to non-negative integer powers (1), multiplied by a constant coefficient (5). However, the term "-2" is not a polynomial because it does not have any variables. Since the given expression has a term that is not a polynomial, it is not considered a polynomial itself.
3.
Is 2/(x+2) a polynomial?
Correct Answer
B. No
Explanation
A polynomial is an algebraic expression with one or more terms, where each term is a product of a constant and a variable raised to a non-negative integer exponent. In this case, the expression 2/(x+2) is not a polynomial because it contains a variable in the denominator, which violates the definition of a polynomial.
4.
Is 3xyz + 3xy^{2}y - 0.1xz - 200y + 0.5 a polynomial?
Correct Answer
A. Yes
Explanation
The given expression is a polynomial because it consists of several terms that are combined using addition and subtraction. Each term is a monomial, which means it is a product of constants and variables raised to non-negative integer exponents. Therefore, the expression satisfies the definition of a polynomial.
5.
Is x/2 a polynomial?
Correct Answer
A. Yes
Explanation
A polynomial is an expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. In this case, x/2 can be considered a polynomial because it is an algebraic expression with a variable (x) and a coefficient (1/2), and it is formed using the operation of division. Therefore, x/2 satisfies the definition of a polynomial.
6.
Is -6x - (7/9)x a polynomial?
Correct Answer
B. Yes
Explanation
The given expression, -6x - (7/9)x, is a polynomial because it is a combination of terms that involve only addition, subtraction, and multiplication of variables raised to non-negative whole number exponents. The expression can be simplified to (-54/9)x - (7/9)x, which further simplifies to (-61/9)x. Since the expression follows the definition of a polynomial, it can be considered as one.
7.
Is √x a polynomial?
Correct Answer
B. No
Explanation
The square root of x is not a polynomial because a polynomial is an expression that consists of variables, constants, and operations such as addition, subtraction, multiplication, and exponentiation. However, the square root of x involves a radical operation, which is not allowed in polynomials. Therefore, the answer is no.
8.
Is 3x/8 a polynomial?
Correct Answer
A. Yes
Explanation
A polynomial is an algebraic expression with one or more terms, where each term consists of a constant multiplied by a variable raised to a non-negative integer power. In the given expression, 3x/8, we have a constant (3) multiplied by a variable (x) raised to the power of 1 (which is a non-negative integer). Therefore, 3x/8 can be considered as a polynomial.
9.
Is 512v^{5} + 99w^{5} + 1 a polynomial?
Correct Answer
A. Yes
Explanation
Yes, the given expression is a polynomial. A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. In this case, the expression consists of variables (v and w), coefficients (512 and 99), and exponents (5). Therefore, it meets the criteria of a polynomial.
10.
Is 5c^{2 }- b^{2}/2 a polynomial?
Correct Answer
B. Yes
Explanation
The expression 5c2 - b2/2 is a polynomial because it is a combination of variables (c and b) raised to non-negative integer powers (2), multiplied by coefficients (5 and 1/2), and added together. A polynomial is a mathematical expression with one or more terms, and each term consists of a variable raised to a non-negative integer power, multiplied by a coefficient, and added or subtracted from other terms. Therefore, the given expression meets the criteria and is a polynomial.