{"id":71117,"date":"2021-04-05T11:22:48","date_gmt":"2021-04-05T16:22:48","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=71117"},"modified":"2026-03-28T12:20:28","modified_gmt":"2026-03-28T17:20:28","slug":"degree-of-polynomials","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/degree-of-polynomials\/","title":{"rendered":"Degree of Polynomials Overview"},"content":{"rendered":"

A polynomial<\/a> is an expression that shows sums and differences of multiple terms made of coefficients and variables.<\/p>\n

A polynomial expression with zero degree is called a constant<\/strong>. A polynomial expression with a degree of one is called linear<\/strong>. A polynomial expression with degree two is called quadratic<\/strong>, and a polynomial with degree three is called cubic<\/strong>.<\/p>\n

Degree of Polynomials Sample Questions<\/a><\/div>\n

Degree of Polynomials with One Variable<\/h3>\n

The degree of a polynomial with one variable is the value of the largest exponent.<\/p>\n

For example, the degree of the polynomial expression \\(3x^5+4x-2\\), is 5 because of the term \\(3x^5\\) that has an exponent of 5.<\/p>\n

Here are some additional examples of polynomial expressions and the degree of the expression:<\/p>\n\n\n\n\n\n\n\n\n\n
Example<\/th>\nDegree<\/th>\n<\/tr>\n<\/thead>\n
\\(12\\)<\/td>\n\\(0\\)<\/td>\n<\/tr>\n
\\(3x-2\\)<\/td>\n\\(1\\)<\/td>\n<\/tr>\n
\\(5x^2-x+7\\)<\/td>\n\\(2\\)<\/td>\n<\/tr>\n
\\(x^3+2x^2-4x-12\\)<\/td>\n\\(3\\)<\/td>\n<\/tr>\n
\\(2x^4-4x^3+x^2-3x-3\\)<\/td>\n\\(4\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Degree of Polynomials with Multiple Variables<\/h3>\n

The degree of a polynomial expression with multiple variables is the degree of the term with the largest degree, which can be calculated by adding the values of the exponents of the variables in that term.<\/p>\n

For example, the degree of the term \\(6x^2y^3\\) is 5 because the exponent of \\(x\\) is 2 and the exponent of \\(y\\) is 3 and \\(2+3=5\\).<\/p>\n

To find the degree of the polynomial expression \\(3x^5 y^3-4x^4 y^2+x^2 y^3-2xy\\), we start by finding the degree of each term:<\/p>\n