A polynomial function is a function such as a quadratic, a cubic, a quadratic, and so on, involving
only non-negative integer powers of x. We can give a general definition of a polynomial, and
define its degree.
2. What is a polynomial?
A polynomial of degree n is a function of the form
f(x) = anxn + an−1xn−1 + . . . + a2x2 + a1x + a0
where the a’s are real numbers (sometimes called the coefficients of the polynomial). Although
this general formula might look quite complicated, particular examples are much simpler. For
f(x) = 4x3
− 3x2 + 2
is a polynomial of degree 3, as 3 is the highest power of x in the formula. This is called a cubic
polynomial, or just a cubic. And
f(x) = x7
− 4x5 + 1
is a polynomial of degree 7, as 7 is the highest power of x. Notice here that we don’t need every
power of x up to 7: we need to know only the highest power of x to find out the degree. An
example of a kind you may be familiar with is
f(x) = 4x2
− 2x − 4
which is a polynomial of degree 2, as 2 is the highest power of x. This is called a quadratic.
Functions containing other operations, such as square roots, are not polynomials. For example,
f(x) = 4x3 + px − 1
is not a polynomial as it contains a square root. And
f(x) = 5x4
− 2x2 + 3/x
is not a polynomial as it contains a ‘divide by x’.
Please watch the fallowing video to reach a better understanding of Polynomial Function: