Question

Factor x^2 + 4x - 21

Answer 1

(x - 3)(x + 7)

Explanation:

x^2 + 4x - 21

=> x^2 + 7x - 3x - 21

=> x(x + 7) -3(x + 7)

=> (x + 7)(x - 3)

Answer 2

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

Explanation:

So we want to factor the expression:

`x^2+4x-21`

When factoring, we want to find two numbers that equals (a)(c) and add up to b. We can then substitute it for b.

So, we want two numbers that when multiplied equals (1)(-21)=-21 and adds up to 4.

We can use 7 and -3.

So:

`x^2+4x-21\\=x^2-3x+7x-21`

Factor out an x from the first two terms, and a 7 from the third and fourth terms:

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

Grouping:

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

And we are done :)