Here are two steps from the derivation of the quadratic formula
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"Classify the polynomial by the number of terms" means a term contains both the variables and its coefficient. For example a "monomial" has one term like .
A binomial has 2 terms like
A trinomial has 3 terms like
And a polynomial has 4 or more terms.
So basically one can classify the type of polynomial by counting the number of terms in a given equation.