Factorization 5

1. Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime.

3x² + 11x + 6

Solution: Factors of 6 are 3*2 or 6*1

Factors of 3 is 3*1

By trial and error method we find, if we take 3x and x as 1st terms :

=(3x + _) (x + _)

Since we have +6 , so sign before 2nd terms will be +,+

So, we check for which factors of 6 we get,

=(3x + 2) (x + 3)

= 3x(x + 3) + 2(x + 3)

= 3x² + 9x + 2x + 6

= 3x² + 11x + 6

So, by trial and error we find the factors = (3x + 2) (x + 3).

2. Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime.

15z² + 11z – 12

Solution: Factors of 12 are 3*4 or 6*2 or 12*1

Factors of 15 are 3*5 or 15*1

By trial and error method we find, if we take 3z and 5z as 1st terms :

(3z + _) (5z - _)

Since we have -12 , so sign before 2nd terms will be +,- or -,+

So, we check for which factors of 12 we get

= (3z + 4) (5z - 3)

= 15z² + 20z -9z -12

= 15z² + 11z – 12

So, by trial and error we find the factors = (3z + 4) (5z - 3).