Example:

1) Factor 4x3 - 12x2 + x - 3

SOLUTION:
Factors of 4: 1, -1, 2, -2, 4, -4  (possible h values)
Factors of -3: 1, -1, 3, -3  (possible k values)

Taking only the positive h values, and all k values, the following are possible
factors of 4x3 - 12x2 + x - 3:
(x + 1), (x - 1), (x + 3), (x - 3)
(2x + 1), (2x - 1), (2x + 3), (2x - 3)
(4x + 1), (4x - 1), (4x + 3), (4x - 3)

Checking:
(x + 1) factor:  k = -1, substitute x = -1 into polynomial:
        4(-1)3 - 12(-1)2 + (-1) -3 = -20  Thus, not a factor

(x - 1) factor: k = 1, sub in x = 1:
        4(1)3> - 12(1)2 + (1) -3 = -10  Thus, not a factor

(x + 3) factor: k = -3, sub in x = -3:
         4(-3)3> - 12(-3)2 + (-3) -3 = -6  Thus, not a factor

(x - 3) factor: k = 3, sub in x = 3:
        4(3)3> - 12(3)2 + (3) -3 = 0  Thus, (x - 3) IS A FACTOR!

Using long division to find other factor(s):

           4x2 + 0x + 1
          -------------------
  (x - 3)| 4x3 - 12x2 + x - 3
           4x3 - 12x2
           ----------
                  0x2 +  x
                  0x2 - 0x
                  ---------
                         x - 3
                         x - 3
                         -----
                           0

Therefore, (x - 3) and (4x2 + 1) are the two factors of 4x3 - 12x2 + x - 3
Return to the tutorial