math analysis
posted by Chelsea on .
is (x^25) a factor of x^43x^21?

Let's compute the remainder of the polynomial after division by x^2  5. So, we want to evaluate:
x^43x^21 Mod (x^2  5)
If we use the equals sign to mean equality Modulo x^2  5 in the following, then we have:
x^2 = 5 >
x^4 = 25
So, we have:
x^4  3 x^2  1 =
25  15  1 = 9
This is nonzero, so x^2  5 is not a factor of the polynomial.