Prime Polynomials
Also called Irreducible Polynomials
Polynomial
A polynomial looks like this:
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| example of a polynomial this one has 3 terms |
Prime Polynomial
In a similar way to Prime Numbers :
A Prime Polynomial cannot be factored any further.
With these special conditions:
- it depends on the number set (integer, real or complex)
- does not include polynomials that are just constants
Factors are what we can multiply together to get our result.
The factors can be different when we choose a different number set!
Example: x2 − 2
Using Integers we cannot factor it any more, so it is a Prime Polynomial
But with Real Numbers we can factor it into:
(x − √2)(x + √2)
Example: x3 − x2 −2x + 2
For Integers it can be factored into:
(x − 1)(x2 − 2)
So it is not a Prime Polynomial.
And with Real Numbers we can go one step further:
(x − 1)(x − √2)(x + √2)