"Polynomial Equations" tends to be an expression used rather loosely and much of the time, incorrectly. In my experience, when a student refers to Polynomial equations, they are in fact referring to polynomials. A polynomial equation is a polynomial put equal to something.
A polynomial is NOT an equation. The equations mostly studied at the elementary math level are linear equations or quadratic equations.
So - onto Polynomials.
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Definition: A Polynomial is a finite sum of monomials.
Some Examples of these would be:
We can classify Polynomials in two ways.
1: By the number of monomials (terms) they contain.
2: By the degree of the Polynomial. The degree of a polynomial with only ONE variable is the highest power to which that variable is raised.
Once you have learned the classification of the polynomial, the next step to take is learning how to add, subtract, multiply and divide polynomials.
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