In order to factor  , first multiply the leading coefficient 5 and the last term 7 to get 35. Now we need to ask ourselves: What two numbers multiply to 35 and add to -2? Lets find out by listing all of the possible factors of 35
Factors:
1,5,7,35,
-1,-5,-7,-35, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 35.
1*35=35
5*7=35
(-1)*(-35)=35
(-5)*(-7)=35
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2
| First Number | | | Second Number | | | Sum | | 1 | | | 35 | || | 1+35=36 | | 5 | | | 7 | || | 5+7=12 | | -1 | | | -35 | || | -1+(-35)=-36 | | -5 | | | -7 | || | -5+(-7)=-12 |
None of these factors add to -2. So the quadratic cannot be factored. |
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