Question 117377


Looking at {{{x^2-3x+7}}} we can see that the first term is {{{x^2}}} and the last term is {{{7}}} where the coefficients are 1 and 7 respectively.


Now multiply the first coefficient 1 and the last coefficient 7 to get 7. Now what two numbers multiply to 7 and add to the  middle coefficient -3? Let's list all of the factors of 7:




Factors of 7:

1,7


-1,-7 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to 7

1*7

(-1)*(-7)


note: remember two negative numbers multiplied together make a positive number



Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">7</td><td>1+7=8</td></tr><tr><td align="center">-1</td><td align="center">-7</td><td>-1+(-7)=-8</td></tr></table>

None of these pairs of factors add to -3. So the expression cannot be factored