Final answer:
The statement that is NOT true about polynomials is that the powers of the variables can be a negative integer. Polynomials must have non-negative integer exponents.
Step-by-step explanation:
The option that is NOT true about polynomials is: c. The powers of the variables can be a negative integer.
Here's a breakdown of each option:
- a. The degree of a polynomial is the highest power of the variable that occurs in the expression. This is a true statement.
- b. A polynomial is written in descending powers of the variable that occurs in the expression. While not a requirement, this is a common practice for readability, so it is usually true.
- c. The powers of the variables can be a negative integer. This is NOT true, as the powers in a polynomial must be non-negative integers.
- d. The leading coefficient of a polynomial is the coefficient attached to the highest degree. This is a true statement and identifies the leading term.
Therefore, to correct the misunderstanding, a polynomial is an algebraic expression consisting of terms with non-negative integer exponents on the variables.