EDGE Math 8

Example

Factor each polynomial.

(a^{2} + 3 a b) + (6 b^{2} + 2 a b)

(3 x^{2} - x) + (12 x - 4)

6 x^{2} + 2 x y - 3 x z - y z

Solution

(a^{2} + 3 a b) + (6 b^{2} + 2 a b)

= a (a + 3 b) + 2 b (3 b + a)

= a (a + 3 b) + 2 b (a + 3 b)

= (a + 3 b) (a + 2 b)

(3 x^{2} - x) + (12 x - 4)

= x (3 x - 1) + 4 (3 x - 1)

= (3 x - 1) (x + 4)

6 x^{2} + 2 x y - 3 x z - y z

= (6 x^{2} + 2 x y) - (3 x z + y z)

= 2 x (3 x + y) - z (3 x + y)

= (3 x + y) (2 x - z)