how to solve "factoring trinomial squares with leading coefficients of 1

Question

6)    2 

     K  +5K-5

 

 

 

11)   2

      R -R+4

 

 

18)   2

      N  -8N-72  

Answer 1

1)  k² + 5k -5

 

Look for factors of the constant, -5, that add to the

coefficient of the k term 5... 

The factors of -5 are  -5,1   or  -1,5

Neither set add to 5 so this is not factorable.

 

2)  R² - R +4

     You are looking for two

     factors of 4 that add to -1.

     The factors of 4 are (-1,-4), (-2,-2), (1,4), (2,2)

     None of the set of factors add to -1, so again, the

     polynomial is not factorable.

 

3)  N² - 8N - 72

     Look for factors of -72 that add to -8..

     -72:  (-1,72), (-2,36), (-3,24), (-4,18), (-6,12), (-8,9)

             (1,-72), (2,-36), (3,-24), (4,-18), (6,-12), (8,-9)

      Again, none of the factor pairs add to -8 so the

      polynomial is not factorable.