How do you factor # 2a^3+4a^2+8a#?

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Answer 1 · 2018-06-14T19:09:14

#2a(a^2+2a+4)#

We immediately recognize that al terms have an #a# in common, so we can factor that out. We get

#acolor(blue)((2a^2+4a+8))#

We also notice that all of the terms I have in blue have a #2# in common that we can factor out. Doing this, we now have

#2acolor(blue)((a^2+2a+4))#

What I have in blue, let's think for a moment:

Are there any two numbers that sum up to #2# and have a product of #4#?

You may have got stuck. There are no such numbers. This means this is the most we can factor this expression with real numbers. Our answer is

#2a(a^2+2a+4)#

Hope this helps!

Answer 2 · 2018-06-14T19:12:16

See a solution process below:

Factor a #color(red)(2a)# form each term in the expression:

#2a^3 + 4a^2 + 8a =>#

#(color(red)(2a) * a^2) + (color(red)(2a) * 2a) + (color(red)(2a) * 4) =>#

#color(red)(2a)(a^2 + 2a + 4)#

The term within the parenthesis cannot be factored further.