Question 117624
Think of {{{9x^2+49}}} as {{{9x^2+0x+49}}}





Looking at {{{9x^2+0x+49}}} we can see that the first term is {{{9x^2}}} and the last term is {{{49}}} 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


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">441</td><td>1+441=442</td></tr><tr><td align="center">3</td><td align="center">147</td><td>3+147=150</td></tr><tr><td align="center">7</td><td align="center">63</td><td>7+63=70</td></tr><tr><td align="center">9</td><td align="center">49</td><td>9+49=58</td></tr><tr><td align="center">21</td><td align="center">21</td><td>21+21=42</td></tr><tr><td align="center">-1</td><td align="center">-441</td><td>-1+(-441)=-442</td></tr><tr><td align="center">-3</td><td align="center">-147</td><td>-3+(-147)=-150</td></tr><tr><td align="center">-7</td><td align="center">-63</td><td>-7+(-63)=-70</td></tr><tr><td align="center">-9</td><td align="center">-49</td><td>-9+(-49)=-58</td></tr><tr><td align="center">-21</td><td align="center">-21</td><td>-21+(-21)=-42</td></tr></table>

None of these pairs of factors add to 0. So the expression cannot be factored