Question

Which expression is not a polynomial?
a) 1/3 x³
b) 12x
c) x² - 2x
d) x³ / 1x

Answer 1

Upon examining and simplifying each expression, all of them - 1/3 x³, 12x, x² - 2x, and x³ / 1x - adhere to the definition of a polynomial; hence, none of the expressions given is not a polynomial. The corrct answer is NONE.

Step-by-step explanation:

To determine which expression is not a polynomial, we need to understand the definition of a polynomial. A polynomial is an expression made up of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Now let's analyze the given expressions:

1. 1/3 x³ - This is a polynomial because it is a single term with a variable raised to a non-negative integer exponent (3) and multiplied by a coefficient (1/3).
2. 12x - This expression is also a polynomial. It is a single term with a variable (x) and a non-zero coefficient (12).
3. x² - 2x - This expression is a polynomial as well. It is comprised of two terms, x² and -2x, each with variables raised to non-negative integer exponents.
4. x³ / 1x - While this might initially look like a polynomial, upon simplification we see that it becomes x² (since x³ divided by x is x²), which is indeed a polynomial. Therefore, all given expressions are actually polynomials.

Based on the definition and the given expressions, it turns out that none of the expressions is not a polynomial. Each expression adheres to the definition of a polynomial by involving only allowable operations and having non-negative integer exponents.