Degree of a Polynomial

Degree of a Polynomial

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Consider the polynomial

\(p\left( x \right):2{x^5} - \frac{1}{2}{x^3} + 3x - \pi \)

The term with the highest power of x is \(2{x^5},\) and the corresponding (highest) exponent is 5. Therefore, we will say that the degree of this polynomial is 5. Thus, the degree of a polynomial is the highest power of the variable in the polynomial. We can represent the degree of a polynomial by \({\rm{Deg}}\left( {p\left( x \right)} \right)\). Some examples:

\[\begin{array}{l}{\rm{Deg}}\left( {{x^3} + 1} \right) = 3\\{\rm{Deg}}\left( {1 + x + {x^2} + {x^3} + ... + {x^{50}}} \right) = 50\\{\rm{Deg}}\left( {x + {\pi ^3}} \right) = 1\end{array}\]

Note from the last example above that the degree is the highest exponent of the variable term, so even though the exponent of π is 3, that is irrelevant to the degree of the polynomial.

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