Question

Which of the following is NOT true about polynomials?

a. The degree of a polynomial is the highest power of the variable that occurs in the expression.

b. A polynomial is written in descending powers of the variable that occurs in the expression.

c. The powers of the variables can be a negative integer.

d. The leading coefficient of a polynomial is the coefficient attached to the highest degree.

Please choose the option that is NOT true about polynomials.

Answer 1

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.