Question

Find the number of factors for the polynomial f x is equal to x power 9 - x

Answer 1

Hello there
The given polynomial is f(x)=x^(9-x)
=(x^9) ×(x^(-x))
=(x^9)×(1/x)^x
Here we can see that there are 9 factors for x^9 and x factors for (1/x)^x.So total number of factors are 9+x.
Hope it Helps.

Answer 2

$f(x)= x^{9} -x = 0$
$x[x^{8} -1] = 0$
$x=0 or x^{8}=1$
$x=0 or x=+-1$

That means there are three factors for the given polynomial
-1, 0 and +1

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