1, x, x^{ 2}, x^{ 3}, … x^{ n}.
Definition: A polynomial is an expression of the form: a_{n} · x^{ n} + a_{n −1} · x^{ n −1} + … + a_{2} · x^{ 2} + a_{1} · x + a_{0},where x is a variable, n is a positive integer and a_{0}, a_{1}, … , a_{n −1}, a_{n} are constants. The highest power of x that occurs is called the degree of the polynomial. The terms are usually written in order from highest power of x to lowest power. 
a_{n} x^{ n} + a_{n −1} x^{ n −1} + … + a_{2} x^{ 2} + a_{1} x + a_{0}
a_{n} x^{ n} + a_{n −1} x^{ n −1} + … + a_{2} x^{ 2} + a_{1} x + a_{0} = 0.(Note that setting y = 0 in the polynomial’s graph means that we are looking at points where the graph crosses the x axis, and setting f (x) = 0 in the polynomial function means that we are looking for values of x for which the output of the polynomial function is zero.
The factor theoremLet f (x) be a polynomial.

The fundamental theorem of algebraOver the complex numbers, a polynomial equation of degree n has exactly n roots. Over the real numbers it may have less than n.

f (0) = 6You should check these. Note that the last three are approximate. Values of x that cause the value of the polynomial to equal zero are called zeros of the polynomial. Thus −2.62, 1.6 and 2.4 are zeros of this polynomial.
f (1) = 9
f (−2.62) = 0
f (1.6) = 0
f (2.4) = 0
x = {−2.62, 1.6, 2.4},or 5 solutions over the complex numbers:
x = {−2.62, 1.6, 2.4, −0.69 − 0.34 i, −0.69 + 0.34 i}.Notice that the two complex number solutions are complex conjugates.
(x + 2.62) (x − 1.6) (x − 2.4) (x^{ 2} + 1.3x + 0.59),or into 5 linear factors over the complex numbers:
(x + 2.62) (x − 1.6) (x − 2.4) (x + 0.69 + 0.34 i) (x + 0.69 − 0.34 i).Notice that letting x = −2.62, 1.6, 2.4, −0.69 − 0.34 i, or −0.69 + 0.34 i causes each factor in turn to become zero, and thus causes the entire product to become zero. These values of x are, of course, just the solutions of the polynomial equation discussed in the previous bullet.
(x − 0)^{ 2} (x + 2.83) (x − 2.83) = 0,then we see that it has roots at x = 2.83 and x = −2.83, as well as a double root at x = 0. This means that the graph of the polynomial function y = x^{ 4} − 8 x^{ 2} should cross the x axis at x = −2.83 and x = 2.83 and it should touch the x axis at x = 0. This can be verified by looking at the red curve shown above.