Question

Which of the following are binomials? Check all that apply.

A. 2 + 3/x
B. x^8
C. 2x^4 + x^2 + 1/2
D. x^11 + 1
E. x^2 + 2
F. x^2 + x + 3

Answer 1

Hints:
To answer this kind of question, we have to understand what a binomial is, and in turn, what makes a "term".
The following definitions explain what they are.

In algebra, a \(binomial\) is a polynomial which is the sum of two \(terms\), which are monomials. It is the simplest kind of polynomial after the monomials.
Examples:
3x+2 is a binomial, 2x is a monomial, x^2+3x+3 is a trinomial, x^3+x^2-2x+3 is a polynomial. In fact, all four examples are also polynomials.

A \(term\) is the product of a constant (positive or negative) multiplied by one or more variables raised to a power. For an expression to be a polynomial, the variables of each term must be raised to a non-negative integer power.
Examples:
-3x^3y^2, +9, 4x^2, 1/x are all terms, but 1/x cannot be part of a polynomial because 1/x = \(x^{-1}\), which is not a positive integer power.