Which statement best demonstrates why the following is a non-example of a polynomial?
33/16 - 62y^2xz-35z^1/3y^2
a. The expression has a variable raised to a negative exponent.
b. The expression has a variable in the denominator of a fraction.
c. The expression has a negative coefficient.
d. The expression has a variable raised to a fraction**
The answer is b.
The correct answer is: b. The expression has a variable in the denominator of a fraction.
A polynomial is an expression that consists of variables, coefficients, and operations such as addition, subtraction, and multiplication. However, in a polynomial, the variables cannot be in the denominator of a fraction. In the given expression, the variable "y" is in the denominator of the fraction 35z^(1/3)y^2. Therefore, this expression is a non-example of a polynomial.
To determine why the given expression is a non-example of a polynomial, let's first understand what a polynomial is. A polynomial is an algebraic expression that consists of variables, coefficients, and exponents, and it only involves addition, subtraction, and multiplication. Each term in a polynomial can have whole number exponents.
Let's analyze the given expression: 33/16 - 62y^2xz - 35z^(1/3)y^2
Here, we can see that the expression has a variable raised to a fraction, z^(1/3)y^2. In a polynomial, the exponents of variables should be whole numbers or zero. Therefore, having a variable raised to a fraction makes this expression a non-example of a polynomial.
Hence, the statement that best demonstrates why the given expression is a non-example of a polynomial is option d. The expression has a variable raised to a fraction.