To factorize a polynomial you need to find the zeros, and then you can write the polynomial as a product of bynomials.
For a polynomial of the form:
[tex]p(x) = A_n*x^n + A_{n-1}*x^{n-1} + ... + A_1*x + A_0[/tex]
We define the zeros as the values of x such that:
p(x) = 0.
On the above case, the degree of the polynomial is n (the maximum exponent). Then the number of zeros of the polynomial is n (same as the degree).
Once we know the n zeros, we can factorize the polynomial as:
[tex]p(x) = A_n*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]
For example, for the polynomial:
[tex]p(x) = 2x^2 - 8[/tex]
The two zeros are x = 2 and x = -2, then it can be rewriten as:
[tex]p(x) = 2*(x + 2)*(x - 2)[/tex]
If you want to learn more about polynomials:
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