# Factoring over ℤ/pℤ[x]: factor factoriser

### 5.34.14 Factoring over ℤ/pℤ[x]: factor factoriser

The factor command factors polynomials with coefficients in ℤ/pℤ. (See also Section 5.12.10.)

- factor takes one argument:
  P, a polynomial with coefficients in ℤ/pℤ (p must be prime).
- factor(P) returns P in factored form.

#### Example.

Input:

factor((-3*x^3+5*x^2-5*x+4)%13)

Output:

⎛ ⎝ | ⎛ ⎝ | −3 | ⎞ ⎠ | %13 | ⎞ ⎠ | ⎛ ⎝ | ⎛ ⎝ | 1%13 | ⎞ ⎠ | x+ | ⎛ ⎝ | −6 | ⎞ ⎠ | %13 | ⎞ ⎠ | ⎛ ⎝ | ⎛ ⎝ | 1%13 | ⎞ ⎠ | x2+6%13 | ⎞ ⎠