SOLUTION: why can't this be factored 9x^2+49

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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 NumberSecond NumberSum
14411+441=442
31473+147=150
7637+63=70
9499+49=58
212121+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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