How do you factor #3x^2 + 4x + 1#?
You find its roots and then turn them into factors, as follows.
Using Bhaskara, let's find the roots:
Now, we can rewrite your function as
There are a few ways to factor
One is essentially trial and error:
We know how to multiply binomials. now we want to find two binomials whose product is
The product of the
The product (multiply) of the constants (the "other numbers" -- and the L in FOIL) must be
So if it can be factored using integers, the factoring must be:
Why do we need to check?
We would have followed exactly the same reasoning to try to factor