John K. answered • 08/17/14

Effective Specialist in Never-Been-Good-at-Math situations

I am not sure that I understood this question, but I decided to list four aspects or ways of categorizing polynomials...I hope this helps.

1) Number of terms in the polynomial: Monomial, binomial, trinomial, etc.

2) Degree of the polynomial: The value of the highest power in the polynomial

3) Classification by degree: Linear if it has degree 1, quadratic if it has degree 2, cubic if it has degree three, etc.

4) Coefficients: The values of the multipliers of the variables in the polynomial. For example, in the quadratic binomial 2

*x*^{2}– (1/3)*x*= 2*x*^{2}+ (–1/3)*x*, the leading coefficient (the coefficient of the degree term) is 2 and the coefficient of the linear term is –1/3.5) Completeness: A complete polynomial has terms of every power up to the degree. For example, a complete cubic polynomial will contain terms with third, second, first

*and*zero power:*x*^{3}+ 2*x*^{2}– (1/2)*x*+ 5 is complete, but*x*^{3}– 2*x*+ 3 is not complete because it doesn't contain an*x*^{2}term.