Classifying Polynomials in Standard Form

Types of Polynomials

• A constant monomial is a polynomial with no variable, represented simply as a number, such as 3.
• A linear monomial has one variable with an exponent of one, exemplified by 4x.
• A linear binomial consists of two terms, each containing the same variable, such as 4x - 7.

Higher Degree Polynomials

• A quadratic monomial includes terms where the highest exponent is 2, such as x^2.
• A quadratic binomial contains two terms, both having a degree of 2, like x^2 + 3.
• A quadratic trinomial has three terms with a highest degree of 2, for example, x^2 + 2x + 1.

Cubic Polynomials

• A cubic monomial consists of one term where the highest exponent is 3, such as x^3.
• A cubic binomial has two terms with a maximum degree of 3, like x^3 + 2x.
• A cubic trinomial contains three terms, each with a degree of 3, e.g., x^3 + x^2 + x.

Higher Degree Classes

• A cubic polynomial is any polynomial with terms up to the third degree, including multiple terms.
• A quartic monomial features one term with a degree of 4, such as x^4.
• A quartic binomial has two terms, both with a degree of 4, for instance, x^4 + x.
• A quartic trinomial is made up of three terms where the highest degree is 4, like x^4 + 2x^2 + 1.
• A quartic polynomial encompasses polynomials with degrees up to four.

Quintic Polynomials

• A quintic monomial singularly focuses on one term with a degree of 5, e.g., x^5.
• A quintic binomial comprises two terms with a maximum degree of 5, such as x^5 + x.
• A quintic trinomial consists of three terms with a highest degree of 5, e.g., x^5 + 2x^3 + 4.
• A quintic polynomial refers to polynomials that may include any number of terms but the highest degree is 5.