Question

How do you factor `t^ { 2} - 4t - 12`?

Answer 1

See explanation below:

Explanation:

To factor this binomial you need to "play" with different multipliers of 12 (1x12, 2x6, 3x4, 6x2, 12x1). Additionally we know it is going to be in form:

`(t - color(red)(a))(t + color(blue)(b))`

Where:
`color(red)(a) > color(blue)(b)` because the `4t` term is negative

`color(red)(-a) + color(blue)(b) = 4`

`color(red)(a) xx color(blue)(b) = 12`

The solution is:

`(t - color(red)(6))(t + color(blue)(2))`