Polynomials
Main Concept
A polynomial is any object created by the addition, subtraction, and multiplication of constants and variables:
x−4⋅y+5+2 x+3 y+π⋅z
x2+x⋅y+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 x2−90
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 x⋅x+y⋅y
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
x2−3x+4
5 x6+4 x2
6
x2−y4
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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