Which of the following describes a trinomial?

Which of the following describes a trinomial?

• A. A polynomial with zero terms
• B. A polynomial with one term
• C. A polynomial with two terms
• D. A polynomial with three terms

Answer: (D)

A trinomial is specifically defined as a polynomial consisting of three distinct terms. This means that in a trinomial, you will have terms combined by addition or subtraction that involve different degrees or constants, such as \( ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants and \( x \) is the variable. In contrast, the other options represent different types of polynomials: a polynomial with zero terms would be classified as the zero polynomial, a polynomial with one term is known as a monomial, and a polynomial with two terms is referred to as a binomial. Each of these categories has its own unique characteristics, but only the trinomial specifically takes the form of having exactly three terms. Thus, the correct description of a trinomial is indeed that it is a polynomial with three terms.

A trinomial is specifically defined as a polynomial consisting of three distinct terms. This means that in a trinomial, you will have terms combined by addition or subtraction that involve different degrees or constants, such as ( ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants and ( x ) is the variable.

In contrast, the other options represent different types of polynomials: a polynomial with zero terms would be classified as the zero polynomial, a polynomial with one term is known as a monomial, and a polynomial with two terms is referred to as a binomial. Each of these categories has its own unique characteristics, but only the trinomial specifically takes the form of having exactly three terms. Thus, the correct description of a trinomial is indeed that it is a polynomial with three terms.