How do I know if this is a polynomial function?
m(x)=(x^2-3x-4)/(x^2+1)
Also...
How would I find the zeros?
Polynomials functions are made of terms that have variables which are raised to whole-number exponents (or else the terms are just plain numbers); there are no square roots of variables, no fractional powers, and no variables in the denominator of any fractions.
These are all polynomials: 6x (one term polynomial), 10x + 7 (bi-nomial, degree 1 polynomial), 7x^2 + 2x -6 (tri-nomial, degree 2 polynomial)
The function you are asking about CAN be a polynomial, but in its present form it is NOT. It is currently a rational function (ratio/fraction) See if you can turn it into a polynomial. HINT: can you cancel anything?
To find the zeroes, see if you can draw a graph of the function after you turn it into a polynomial
Good luck!
The function $\displaystyle \frac{x^2 - 3x - 4}{x^2 + 1}$ is NOT a polynomial function.
It CANNOT be 'turned into' a polynomial function by cancelling anything.
The zeroes of $\displaystyle \frac{x^2 - 3x - 4}{x^2 + 1}$ are found by solving $\displaystyle x^2 - 3x - 4 = 0$.
Finding the zeroes of a function is usually required in order to actually sketch the graph of a function in the first place.