Factoring Completely Solutions

To factor completely, combine multiple factoring methods until an expression cannot be factored any further.

Example 1

Factor completely.

$4 x^{2} - 4 x - 3$

$(4 x^{2} - 6 x) + (2 x - 3) 2 x (2 x - 3) + 1 (2 x - 3) (2 x - 3) (2 x + 1)$

Example 2

Factor completely.

$4 x^{3} - 6 x^{2} - 36 x + 54$

$2 (2 x^{3} - 3 x^{2} - 18 x + 27) 2 ((2 x^{3} - 3 x^{2}) + (- 18 x + 27)) 2 (x^{2} (2 x - 3) - 9 (2 x - 3)) 2 (2 x - 3) (x^{2} - 9) 2 (2 x - 3) (x - 3) (x + 3)$

Example 3

Factor completely.

$- 8 x^{2} + 200$

$- 8 (x^{2} - 25) - 8 (x - 5) (x + 5)$