Question

How do you factor completely: `2x^3 + 14x^2 + 6x + 42`?

Answer 1

`2(x+7)(x^2+3)`

Explanation:

Notice that, if you factor out `2x^2` from the first two members and factor out `6` from the last two members of this equation, you will have the same in both remainders - `(x+7)`:
`2x^3+14x^2+6x+42=2x^2(x+7)+6(x+7)`

Now we can use the distributive law and factor out `(x+7)` getting:
`(x+7)(2x^2+6)=2(x+7)(x^2+3)`