In order to factor  , first multiply the leading coefficient 4 and the last term 13 to get 52. Now we need to ask ourselves: What two numbers multiply to 52 and add to 16? Lets find out by listing all of the possible factors of 52
Factors:
1,2,4,13,26,52,
-1,-2,-4,-13,-26,-52, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 52.
1*52=52
2*26=52
4*13=52
(-1)*(-52)=52
(-2)*(-26)=52
(-4)*(-13)=52
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 16
| First Number | | | Second Number | | | Sum | | 1 | | | 52 | || | 1+52=53 | | 2 | | | 26 | || | 2+26=28 | | 4 | | | 13 | || | 4+13=17 | | -1 | | | -52 | || | -1+(-52)=-53 | | -2 | | | -26 | || | -2+(-26)=-28 | | -4 | | | -13 | || | -4+(-13)=-17 |
None of these factors add to 16. So the quadratic cannot be factored. |
(