Question
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
$p^2 q+p q^2$
$p^2 q+p q^2$
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Answer
Definitions: A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms.
A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial $p^2 q+p q^2$ has exactly two terms, i.e.,$p^2 q$ and $p q^2$. Therefore, it is a binomial.
A polynomial is a trinomial if it has exactly three non-zero terms. The polynomial $p^2 q+p q^2$ has exactly two terms, i.e.,$p^2 q$ and $p q^2$. Therefore, it is a binomial.
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