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!