Question 117624: why can't this be factored
9x^2+49
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Think of  as 
Looking at we can see that the first term is  and the last term is  where the coefficients are 9 and 49 respectively.
Now multiply the first coefficient 9 and the last coefficient 49 to get 441. Now what two numbers multiply to 441 and add to the middle coefficient 0? Let's list all of the factors of 441:
Factors of 441:
1,3,7,9,21,49,63,147
-1,-3,-7,-9,-21,-49,-63,-147 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 441
1*441
3*147
7*63
9*49
21*21
(-1)*(-441)
(-3)*(-147)
(-7)*(-63)
(-9)*(-49)
(-21)*(-21)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 0? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 0
| First Number | Second Number | Sum | | 1 | 441 | 1+441=442 | | 3 | 147 | 3+147=150 | | 7 | 63 | 7+63=70 | | 9 | 49 | 9+49=58 | | 21 | 21 | 21+21=42 | | -1 | -441 | -1+(-441)=-442 | | -3 | -147 | -3+(-147)=-150 | | -7 | -63 | -7+(-63)=-70 | | -9 | -49 | -9+(-49)=-58 | | -21 | -21 | -21+(-21)=-42 |
None of these pairs of factors add to 0. So the expression cannot be factored
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