Question

How do you factor quadratic equations like `x^2 + 4x -21`?

Answer 1

Factoring is sometimes more straightforward than other times but here's the thing, you need to ensure that you have the number on either end add up to the middle term which is 4x.

So let start off factoring the quadratic equation.

You assume that there are two binomials which you would have
(`x+`something)(`x+`something)

So we know that from this step, we have `x^2` already but how do I get `-21`?

Now think of factors that get you `-21` but also that add up to `4`.

`-7x*3=-21`
`-7+3=-4`
This combination doesn't work but let try another one.

`7x*-3=-21`
`7+(-3)=4`

So this combination work, let plug it back into the equation

`(x+7)(x-3)`

Now, let double check that it works.
`(x+7)(x-3)`
`x^2-3x+7x-21`
`x^24x-21 rarr` Combining like terms

`7` and `-3` works to factor this quadratic equation.