Looking at we can see that the first term is and the last term is where the coefficients are 1 and 5 respectively.
Now multiply the first coefficient 1 and the last coefficient 5 to get 5. Now what two numbers multiply to 5 and add to the middle coefficient 6? Let's list all of the factors of 5:
Factors of 5:
1,5
-1,-5 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 5
1*5
(-1)*(-5)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 6
First Number
Second Number
Sum
1
5
1+5=6
-1
-5
-1+(-5)=-6
From this list we can see that 1 and 5 add up to 6 and multiply to 5
Now looking at the expression , replace with (notice adds up to . So it is equivalent to )
Now let's factor by grouping:
Group like terms
Factor out the GCF of out of the first group. Factor out the GCF of out of the second group
Since we have a common term of , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
(