Question

How do you factor `3t^2-8t+4`?

Answer 1

`(3t-2)(t-2)`

Explanation:

3 is a prime number so we can only have: `(3t+-?)(t+-?)`

The whole number factors of 4 are: 1 and 4 also 2 and 2
As the 4 is positive then both the ? must be of the same sign
As the 8 is negative it implies that both the ? are negative

Lets try:

`(3t-1)(t-4) -> 3t^2-12t-t +4 color(red)(" Fail")`

Lets try

`(3t-2)(t-2)->3t^2-8t+4 color(red)(" Works")`