



 
Hi Geri, Let's try x^{2}  25 first.
I know this because if you multiply (x  5) by (x + 5) and simplify you get x^{2}  25. This means that for any number x, x^{2}  25 = (x  5)(x + 5). For example if x = 12 then
Now what about x^{2} + 25? If x = 2 for example then x^{2} + 25 = 4 + 25 = 29 which is a prime number. Thus the only factors of 29 are 29 and 1 and hence the only factorization of 29 is 29 × 1. Similarly if x = 4 then x^{2} + 25 = 41 which is again prime. Hence the only factorization of x^{2} + 25 which is valid for every number x is
This is certainly not what you are looking for and thus we say x^{2} + 25 doesn't factor. Penny  


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