Polynomials

Generally, polynomials are functions of

f (x) = a_nxⁿ + a_n-1x^n-1 + ... + a₁x + a₀,

where
n is the degree of the polynomials and it must be positive integer,
a_n is the leading coefficient of the polynomials and
a_i are coefficients.

Table below shows some examples of polynomials:

Function	Degree	Leading Coefficient	Type of Polynomial
4	0	4	Constant
5x + 1	1	5	Linear
25 - x2	2	-1	Quadratic
(x-1)2(1-2x)	3	-2	Cubic
(x-1)2(3x-1)2	4	9	Quartic

The domain for polynomial is always (-∞,∞); while the range is also (-∞,∞) for odd degree but for even degree we have to find it according to the function given. The graph shown below are the basic form of polynomials: f (x) = xⁿ and g(x) = -xⁿ. Try to slide the value of n to look at different types of the polynomials.

Betty, Created with GeoGebra