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Polynomials

Main Concept

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

  x4y+5+2 x+3 y+πz 

x2+xy+y2 

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): 

5 x2

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

3 x5 +3 x3+2 x290

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

x2+y2 instead of xx+yy

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

Term

Degree

5 x4

4

3x2

2

x2y3

5

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

Polynomial

Degree

x23x+4

2

5 x6+4 x2

6

x2y4

4

 

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

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