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

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Answer 1 · 2018-08-03T12:55:24

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

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

Grouping;

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

Factoring;

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

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

Answer 2 · 2018-08-03T23:19:12

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

Let's look at our quadratic as two parts:

$x^{2} + 3 x + 4 x + 12$ $color(steelblue)(x^2+3x)+color(purple)(4x+12)$

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

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

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

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

Hope this helps!

How do you factor x2+3x+4x+12x^2+3x+4x+12 by grouping?