Polynomials - Maple Help

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Polynomials

Main Concept

A polynomial is any object created by the addition, subtraction, and multiplication of constants and variables:

${x}^{2}+x\cdot y+{y}^{2}$

A monomial is the product of a constant (for example, 5,-90,40) and a number of variables or indeterminates (for example, x, y, z): 

A polynomial can always be written as the sum of a finite number of monomials (or terms). This is called expanded form:

When the same variable occurs more than once in such a term, you can use an exponent to represent this in the product:

${x}^{2}+{y}^{2}$ instead of $x\cdot x+y\cdot y$

The degree of a term is the sum of the powers of each variable in the term:

 Term Degree $4$ $3{x}^{2}$ $2$ ${x}^{2}{y}^{3}$ $5$

The degree of a polynomial is the maximum degree of any of its nonzero terms:

 Polynomial Degree ${x}^{2}-3x+4$ $2$ $6$ ${x}^{2}-{y}^{4}$ $4$

Use the slider to choose the degree of the polynomial. Choose whether to display the power function ${x}^{n}$, or a polynomial with the maximum number of roots possible. The polynomial and its name will be displayed.

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