Question

How do you factor `x^2+3x-4=0`?

Answer 1

`(x-1)(x+4)`

Explanation:

In order to determine the factorised form of the given equation we must determine the factors of the `+3x+ and the`-4# coefficients:

For the `+3x` value:

The only factors of 3 (as it is a prime number) are `3` and `1`:

For the `-4` coefficient:

The factors of `-4` are:

`-4` and `1`
`4` and `-1`
`-2` and `2`
`2` and `-2`

If we consider that in the factorised form the sum of two factors of the `-4` term must equal `+3`, then we can determine that the required values are `-1` and `4` as these are the only values that when added form `+3`:

As a result, the factorised form of the given equation is:

`(x-1)(x+4)`