A polynomial of the type P(x) = a0x3 + a1x2 +a2x+ a3 , where a0 ? 0 is called a third degree polynomials or a cubic polynomial. Below is the example on third degree polynomial finding the roots of given polynomial.
Note: In the above definition it is important that a0 ? 0 otherwise it becomes a quadratic or a linear polynomial.
Examples:
f (x) = x3 + 2x2 + x + 1
g (x) = x3
h (x) = -2x3 + 5
In short, these are all the polynomials where the highest power of x is 3.
Factoring a Cubic or third Degree Polynomial
As the name suggests a cubic equation will be of the form a0x3 + a1x2 +a2x+ a3 = 0, a0 ? 0.
This equation will have 3 roots as the degree is 3.
A cubic equation will always have at least one real root. The remaining 2 roots may be real or complex numbers.
If all the roots are real the graph will look something like this:
As you can see, it cuts the x-axis at 3 distinct points.
If only one root is real the graph will be as follows:
It cuts the x-axis only at 1 point.
In the next sections we will also work on the methods to solve a cubic equation.
Related Tags
Third Degree Polynomial , Third Degree Polynomial concept , Third Degree Polynomial expression