Question

How do you factor the expressions `x^2+3x-4`?

Answer 1

`x_1=-4`
`x_2=1`,
You use the so called discriminant

Explanation:

Most of the quadratic equations have the form of: `ax^2+bx+c=0`
In your case: a=1 , b=3, c=-4
Then we use the discriminant `D=b^2-4*a*c`
In this case:
`D=3^2-4*1*(-4)`
We get the result: D=25
Now we need the roots, for which we use the equation:
`x_1=(-b-sqrt(D))/(2*a)`
`x_2=(-b+sqrt(D))/(2*a)`
We get:
`x_1=-4`
`x_2=1`
And that's all :)

Answer 2

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

Explanation:

What tow numbers sum up to our middle term of `3`, and have a product of `-4` (the last term)?

After some trial and error, we arrive at `-1` and `4`. So we can factor our quadratic as

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

Hope this helps!