how do i factor s^2+4st-12t^2

Question

s²+4st-12t²

Answer 1

s² + 4st -12t² = 0

 

Find two numbers such that;

 

m x n = -12t²

m + n = 4t

 

the possible combinations for m x n = -12t² are:

(-12t, t) or (-6t, 2t) or (-4t, 3t) or 

(12t, -t) or (6t, -2t) or (4t, -3t)

 

but, the one which satisfies m + n = 4t is (6t, -2t), therefore, the factors are:

 

s² + 4st -12t² = (s + 6t) (s -2t)

 

Answer 2

First you see which two numbers are a factor of 12 that equals 4. In this case, it is 6-2. Then you factor

(s²+6st) (-2st-12t²).

 

Answer 3

Kevin,

      By inspection 6 and 2 look like good choices for the coefficients of t so try (s+6t)(s-2t) or (s-6t)(s+2t) as you can see the first choice is the only one that gives s²+4st-12t² when expanded.

 

Jim