How-to 7 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

Factor[x ^ 3 - 3x ^ 2 - 2x + 6]

Output

(-3 + x)*(-2 + x^2)

Step 2

Factor[x ^ 3 - 3x ^ 2 - 2x + 6, Extension -> Sqrt[2]]

Output

Factor[6 - 2*x - 3*x^2 + x^3, Extension -> Sqrt[2]]

Step 3

Factor[x ^ 3 - 3x ^ 2 - 2x + 6, Modulus -> 3]

Output

x*(1 + x^2)

Step 4

Factor[x ^ 3y ^ 2 - 3x ^ 2y - 2x y ^ 3 + 6y ^ 2]

Output

-(y*(-x^2 + 2*y)*(-3 + x*y))

Step 5

IrreduciblePolynomialQ[x ^ 2 + x + 1]

Output

True

Step 6

PolynomialGCD[x ^ 2 - 1, x ^ 2 + 2x + 1, x ^ 3 - x ^ 2 - x + 1]

Output

1 + x

Step 7

Roots[x ^ 3 - 3x ^ 2 - 2x + 6 == 0, x]

Output

x == -Sqrt[2] || x == Sqrt[2] || x == 3

Factor a polynomial

Functions used