Answer
To factor a polynomial completely the process is similar to prime factorization of integers. A polynomial is said to be prime if it cannot be expressed as a product of other polynomials.
Completely factored polynomial is written as a product of monomial factors and prime polynomials having at least two terms.
Taking polynomial for example, $x^{4}$ + 4$x^{3}$ + 6$x^{2}$ + 4 x + 1
complete factors = (x + 1) (x + 1) (x + 1) (x + 1)
Work Step by Step
To factor a polynomial completely the process is similar to prime factorization of integers. A polynomial is said to be prime if it cannot be expressed as a product of other polynomials.
Completely factored polynomial is written as a product of monomial factors and prime polynomials having at least two terms.
For example $x^{4}$ + 4$x^{3}$ + 6$x^{2}$ + 4 x + 1
complete factors = (x + 1) (x + 1) (x + 1) (x + 1)
There is no further factorisation
