Question

Is it possible to factor `y= x^2 + 4x -21`? If so, what are the factors?

Answer 1

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

Explanation:

`"the factors of - 21 which sum to + 4 are + 7 and - 3"`

`x^2+4x-21=(x+7)(x-3)`

Answer 2

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

Explanation:

You can do it solving: `x^2+4x-21=0`

`x^2+4x-21=0`

`a=1, b=4, c=-21`

`x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}`

`x=\frac{-(4)\pm \sqrt{(4)^2-4(1)(-21)}}{2(1)}`

`x=\frac{-4\pm \sqrt{16+84}}{2(1)}`

`x=\frac{-4\pm \sqrt{100}}{2}`

`x=\frac{-4\pm 10}{2}`
then
`x_1=\frac{-4+10}{2}=\frac{6}{2}=3`
`x_2=\frac{-4-10}{2}=\frac{-14}{2}=-7`
And

`x^2+bx+c=(x-x_1)(x-x_2)`
Or
`x^2+4x-21=(x-3)(x-(-7))`

`x^2+4x-21=(x-3)(x+7)`
Q.E.D.