<P> The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients . The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer . The term order has been used as a synonym of degree but, nowadays, may refer to several other concepts (see order of a polynomial). For example, the polynomial 7 x 2 y 3 + 4 x − 9, (\ displaystyle 7x ^ (2) y ^ (3) + 4x - 9,) which can also be expressed as 7 x 2 y 3 + 4 x 1 y 0 − 9 x 0 y 0, (\ displaystyle 7x ^ (2) y ^ (3) + 4x ^ (1) y ^ (0) - 9x ^ (0) y ^ (0),) has three terms . The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0 . Therefore, the polynomial has a degree of 5, which is the highest degree of any term . </P> <P> To determine the degree of a polynomial that is not in standard form (for example: (x + 1) 2 − (x − 1) 2 (\ displaystyle (x + 1) ^ (2) - (x-1) ^ (2))), one has to put it first in standard form by expanding the products (by distributivity) and combining the like terms; for example (x + 1) 2 − (x − 1) 2 = 4 x (\ displaystyle (x + 1) ^ (2) - (x-1) ^ (2) = 4x) is of degree 1, even though each summand has degree 2 . However, this is not needed when the polynomial is expressed as a product of polynomials in standard form, because the degree of a product is the sum of the degrees of the factors . </P>

Polynomial based on degree and number of terms
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