Question 117629


Looking at {{{x^2-4x+16}}} we can see that the first term is {{{x^2}}} and the last term is {{{16}}} where the coefficients are 1 and 16 respectively.


Now multiply the first coefficient 1 and the last coefficient 16 to get 16. Now what two numbers multiply to 16 and add to the  middle coefficient -4? Let's list all of the factors of 16:




Factors of 16:

1,2,4,8


-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations


These factors pair up and multiply to 16

1*16

2*8

4*4

(-1)*(-16)

(-2)*(-8)

(-4)*(-4)


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



Now which of these pairs add to -4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -4


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">16</td><td>1+16=17</td></tr><tr><td align="center">2</td><td align="center">8</td><td>2+8=10</td></tr><tr><td align="center">4</td><td align="center">4</td><td>4+4=8</td></tr><tr><td align="center">-1</td><td align="center">-16</td><td>-1+(-16)=-17</td></tr><tr><td align="center">-2</td><td align="center">-8</td><td>-2+(-8)=-10</td></tr><tr><td align="center">-4</td><td align="center">-4</td><td>-4+(-4)=-8</td></tr></table>

None of these pairs of factors add to -4. So the expression cannot be factored