factor 12t squared-4t-5

Question

How do you factor 12t^2-4t-5

Answer 1

12t²-4t-5=(at±1)(bt∓5)=abt²∓5at±bt-5=abt²±(b-5a)t-5, where a and b are constants to be found.

So ab=12 and |b-5a|=|-4|=4, that is, the difference between b and 5a is 4, and we can sort out the signs later.

The factors of 12 are (a,b)=(1,12), (2,6) or (3,4), so we can make a table to test all these possibilities:

a	b	|b-5a|
1	12	7
2	6	4
3	4	11

The highlighted numbers are clearly the ones we need because the required difference of 4 matches the actual coefficient.

So we have (2t±1)(6t±5)=12t²±(6-10)t-5=12t²±(-4)t-5. We need the middle term to be -4t so we can now replace ± with + and ∓ with -.

Therefore the factorisation is: (2t+1)(6t-5).