Question

How do you factor `6a^3+13a^2+5a`?

Answer 1

`a(2a+1)(3a+5)`

Explanation:

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

`=a(6a^2+13a+5)`

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

`"the factors of the product "6xx5=30`

`"which sum to "+13" are "+3" and "+10`

`"split the middle term using these factors"`

`6a^2+3a+10a+5larrcolor(blue)"factor by grouping"`

`=color(red)(3a)(2a+1)color(red)(+5)(2a+1)`

`"take out the "color(blue)"common factor "(2a+1)`

`=(2a+1)(color(red)(3a+5))`

`6a^3+13a^2+5a=a(2a+1)(3a+5)`