# Math Help - Canonical Decomp 2

1. ## Canonical Decomp 2

Is there an easy way to approach this number or just start dividing away?

10,510,100,501

2. Originally Posted by dwsmith
Is there an easy way to approach this number or just start dividing away?

10,510,100,501
Hint: $(x^2+1)^5 = x^{10} + 5x^8 + 10x^6 + 10x^4 + 5x^2 + 1$.

3. I am not sure how that is supposed to help, but if I could see the connection, how would I know to come up with $(x^2+1)^5$?

4. Originally Posted by dwsmith
I am not sure how that is supposed to help, but if I could see the connection, how would I know to come up with $(x^2+1)^5$?
Second (blatant) hint: Try putting x = 10 in that binomial expansion.

I have to admit that I cheated in order to find that method. I plugged the number 10510100501 in here in order to find the factors. When I saw the answer I could see why it came out that way.