Polynomial Functions

A polynomial function is one that can be written in the form

a_nx + a_n-1x^n-1+…+a₃x³+a₂x² + a₁x+ a₀

_{Where n is an non negative integer, x is a variable, and each of}  a₀,a₁,a₂,…a_n is a constant called a coefficient. 

 Rational Functions:
Find the domain of each rational function
1) f(x) = 1/x²
The domain of  f(x) = 1/x² is the set of all real numbers except x = 0 because the denominator is 0 when x=0, making the fraction undefined
2) g(x) = x² + 3x + 1/x²-x-6
The domain of g(x) = x² + 3x + 1/x²-x-6 is the set of all real numbers except the solutions of x²-x-6=0. Because x²-x-6 factors into (x+2)(x-3), the solutions to x²-x-6=0 are x=-2 and x=3. Therefore, the domain of g is the set of all real numbers except x = -2 and x=3



 Real Functions:


Synthetic Division: