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A rational function is the quotient of two polynomial functions.
A power function is of the form xa where a is a real number. A polynomial function is of the form anxn + an-1xn-1 + ... + a1x + a0 for some positive integer n, and all the ai are real constants.
As with most advanced math, if your "real life" involves engineering work, you will use such math; otherwise, you will hardly have anything to do, in this case, with polynomial functions.
Basically, an expression is not a polynomial when anything is done that is not allowed in a polynomial - for example, use any variable in the denominator of a monomial, use non-integral powers or radicals (which is basically the same as a non-integral power), use functions, etc.
Substitute that value of the variable and evaluate the polynomial.
Yes, all polynomial functions are continuous.
In the 1880s, Poincaré created functions which give the solution to the order polynomial equation to the order of the polynomial equation
None, except that they are functions of one or more variables.
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1 2 3 and 4 are 4 numbers, they are not functions of any sort - cubic polynomial or otherwise.
To factorize a third degree polynomial you need to find the common factor and then group the common terms in order to solve. If no common factor, find the first factor and it becomes a matter of trial and error. The easiest way to do this is to use a graphing calculator.
A rational function is the quotient of two polynomial functions.
A device that was designed to tabulate polynomial functions
That's the definition of a "rational function". You simply divide a polynomial by another polynomial. The result is called a "rational function".
You set x = 0 and evaluate the polynomial. Note that this should be "y-intercept" in the singular, not in the plural.
The way you can use graphs of polynomial functions to show trends in data is by comparing results between different functions. The alternation between the data will show the trends. Time can also be used to show the amount of variation.