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

Aug 2, 2016

$\left(x - 1\right) \left(x + 4\right)$

#### Explanation:

In order to determine the factorised form of the given equation we must determine the factors of the $+ 3 x + \mathmr{and} t h e$-4# coefficients:

For the $+ 3 x$ 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:

$\left(x - 1\right) \left(x + 4\right)$