Question

Determine whether the following expressions are polynomials. If not, provide an explanation.

a. 1
b. 2VX + 16x - 9

Answer 1

Expression (a) 1 is a polynomial of degree zero, and expression (b) 2VX + 16x - 9 is not a polynomial because it contains a square root of a variable, which is against the definition of polynomials.

Step-by-step explanation:

In mathematics, particularly in algebra, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involve only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. To determine whether the given expressions are polynomials:

1. 1 is indeed a polynomial because it can be considered a polynomial of degree zero (it's just a constant term).
2. 2VX + 16x - 9 is not a polynomial. The term 2VX (which likely meant 2√x or 2√x) includes a square root of a variable, which is not allowed in a polynomial expression. Polynomials must have variables raised to whole-number exponents.

Therefore, expression (a) is a polynomial while expression (b) is not because it contains a square root of a variable.