Now lets concentrate on the quadratic inside the parenthesis and ignore the -1 outside the parenthesis (we'll place it back in later)
In order to factor , first multiply the leading coefficient 1 and the last term 3 to get 3. Now we need to ask ourselves: What two numbers multiply to 3 and add to 4? Lets find out by listing all of the possible factors of 3
-1,-3, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 3.
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4
We can see from the table that 1 and 3 add to 4. So the two numbers that multiply to 3 and add to 4 are: 1 and 3
So the original quadratic
breaks down to this (just replace with the two numbers that multiply to 3 and add to 4, which are: 1 and 3)
Group the first two terms together and the last two terms together like this:
Factor a 1x out of the first group and factor a 3 out of the second group.
Now since we have a common term we can combine the two terms.
Combine like terms.
Remember we factored out a negative 1 to start the problem, so lets reintroduce it back in. So our answer is