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

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Answer 1 · 2018-08-03T12:55:24

$(x + 3) (x + 4)$

$x^2 + 3x + 4x + 12$

Grouping;

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

Factoring;

$x(x + 3) +4(x + 3)$

$(x + 3) (x + 4)$

Answer 2 · 2018-08-03T23:19:12

$(x+3)(x+4)$

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!

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