Express the cubic polynomial in the standard form of: ax^3 + bx^2 + cx +d, where "^" implies "raised to the power of." Note that "b," "c" or "d" may be zero but "a" cannot be. Otherwise, the polynomial is no longer a cubic.
Separate the terms into two groups of the form (ax^3 + bx^2) + (cx +d).
Extract, in turn, the greatest common factor, or GCF, of each of the first group: (ax^3 + bx^2) and the second: (cx + d) separately, where they exist, and express each group in factored form. Note that x^2 will be part of any factor of the first group of terms.
Extract the GCF, where it exists, of the first and second groups combined. The ideal result will be in the form: (x - g)(x - h)(x - i), although this may not be achievable in all cases. Multiply out the terms to verify the correctness of the factoring.
Look for an obvious factor of the polynomial. The Factor Theorem states that if a polynomial f(x) has a root g, such that f(g) = 0, then that polynomial has a factor (x - g).
Try, in turn, values such as 0, +1, -1, +2, -2. Where a value, say x = g, is found that reduces the polynomial to zero, divide the original polynomial by (x - g) and factor the results in the form (x - g)(px^2 + qx + r). Note that the polynomial in the second bracket is now a quadratic.
Repeat Step 1 to see if there is another obvious factor for the quadratic polynomial, and factor this out to give the ideal form of (x - g)(x - h)(x - i).
Use the quadratic formula of (-q + or -- √(q^2 - 4pr))/2p, for the quadratic polynomial in Step 1, if no further factors are found in Step 2. This will give the other two factors: (-q + √(q^2 - 4 pr))/2p and (-q - √(q^2 - 4pr))/2p.