Factoring Using Greek Method

Factor: 9z 2 − 12z + 4

Solution:

Step 1: Multiply 9 and 4, that gives 36.

Step 2: Find two factors 36 that sum to -12.

The two factors are -6 and -6, since -6 - 6 = -12 and -6 * -6 = 36.

Step 3: Use these factors from Step 3 to re-write the middle coefficient:

9z 2 − 6z − 6z + 4

Step 4: Group the first two terms and last two terms.

(9z 2 − 6z) + (−6z + 4)

Step 5: Factor out 3 from the first set of parenthesis. Factor out -2 from the second set of parenthesis.

3z(3z − 2) − 2(3z − 2)

Step 6: Factor out (3z − 2)

(3z - 2)(3z - 2)