Question

How do you factor `x^2+3x+4x+12` by grouping?

Answer 1

`(x + 3) (x + 4)`

Explanation:

`x^2 + 3x + 4x + 12`

Grouping;

`(x^2 + 3x) (+4x + 12)`

Factoring;

`x(x + 3) +4(x + 3)`

`(x + 3) (x + 4)`

Answer 2

`(x+3)(x+4)`

Explanation:

Let's look at our quadratic as two parts:

`color(steelblue)(x^2+3x)+color(purple)(4x+12)`

We see that the blue terms have an `x` in common, and the purple terms have a `4` in common, so we can factor that out to get

`color(steelblue)(x(x+3))+color(purple)(4(x+3))`

We now see that both terms have an `x+3` in common, so we can finally factor that out to get

`(x+3)(x+4)`

Hope this helps!