Which expression is a polynomial????
A: 11 0ver the square root of x
B: square root of 11 times x
C: x - square root 11
D: 11 over the square root of x to the 2nd power
(sorry I am not sure how to insert square root symbols or fractions, so u have to imaging its there) thank you!!
A polynomial must have a non-negative integer exponent.
A and B contain square roots or exponents of 1/2
D: 11/(√x)^2
= 11/x or 11 x^-1
so none is a polynomial
C: x - √11
yup, I would go with that one
To determine which expression is a polynomial, we need to understand the definition of a polynomial. A polynomial is an algebraic expression made up of variables, constants, and the operations of addition, subtraction, and multiplication, with non-negative integer exponents.
Now let's analyze each expression:
A: 11 over the square root of x
This expression contains a square root in the denominator, which means it has a rational exponent. Hence, it is not a polynomial.
B: square root of 11 times x
Similarly, this expression contains a square root, which is not in the context of a polynomial. Therefore, it is not a polynomial.
C: x - square root 11
This expression only involves variables (x) and constants (square root of 11), and the operations of addition and subtraction. Therefore, it is a polynomial.
D: 11 over the square root of x to the 2nd power
This expression also contains a square root in the denominator, making it a rational exponent. Hence, it is not a polynomial.
So, the expression that is a polynomial is C: x - square root 11.