(Follow these steps to insure the easiest and most complete factoring of any polynomial)
1. Always Check for a Common Term:
a. 2 x 2 –6x-12 2(x2-3x-6)
b. x2-7x x(x-7)
2. Count the terms:
a. If there are only two (2) terms
1. Difference of 2 perfect squares: x2-16 (x-4)(x+4)
2. Sum of 2 perfect squares: x2+16 NOT Factorable
3
3. Difference of 2 perfect cubes: x -27 (x-3)(x2+3x+9)
4. Sum of 2 perfect cubes: x3+27 (x+3)(x2-3x+9)
b. If there are three (3) terms This sign chart may also be helpful.
1. x +5x+6 (x+3)(x+2)
2
+ + (+)(+)
2. x2-5x+6 (x-3)(x-2) - + (-)(-)
3. x2+x-6 (x+3)(x-2) + - biggest(+)(-)
4. x2-x-6 (x-3)(x+2) - - biggest(-)(+)
If the coefficient of x2 is not 1
follow the same rules but include the first term in calculations. For
example: 10x2 +29x-21 (2x+7)(5x-3)
c. If there are four (4) terms try factoring by grouping
x3-2x2-9x+18 (x3-2x2) + (-9x+18)
x2(x-2) -9(x-2)
(x2-9)(x-2)
(x-3)(x+3)(x-2)
3. If the terms are in quadratic form try substitution
x4-5x2+6 let q= x2 and substitute so that
q2-5q+6
(q-3)(q-2)
then re-substitute and (x2-3)( x2-2)
4. Last Resort is the remainder theorem and synthetic division. Don’t
forget: +/-last divided by +/- first
Created: 4-28-06