Question

How do you factor `6a^3+ 8a^2+ 2a`?

Answer 1

`2a(a+1)(3a+1)`

Explanation:

`"take out a "color(blue)"common factor "2a`

`=2a(3a^2+4a+1)`

`"factor the quadratic using the a-c method"`

`"the factors of the product "3xx1=3`

`"which sum to + 4 are + 3 and + 1"`

`"split the middle term using these factors"`

`3a^2+3a+a+1larrcolor(blue)"factor by grouping"`

`=color(red)(3a)(a+1)color(red)(+1)(a+1)`

`"take out the "color(blue)"common factor "(a+1)`

`=(a+1)(color(red)(3a+1))`

`6a^3+8a^2+2a=2a(a+1)(3a+1)`