SOLUTION: why can't this be factored x^2-4x+16

Question 117629: why can't this be factored
x^2-4x+16
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is 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

First Number	Second Number	Sum
1	16	1+16=17
2	8	2+8=10
4	4	4+4=8
-1	-16	-1+(-16)=-17
-2	-8	-2+(-8)=-10
-4	-4	-4+(-4)=-8

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