Question

Find 5 number of factors for the polynomial f(x)=x^9-x find the factors

Answer 1

Answer:

For the polynomial f(x)=$x^{9}-x$

By Using the formula :

$x^{3} -y^{3} = (x-y) (x^{2} +xy+y^{2} )$

$(x^{3} )^{3} -x^{3} = (x^{3} -x)(x^{6} +x^{4}+x^{2} )$

So $x^{3}$, $x$ , $x^{6}$, $x^{4}$ and $x^{2}$ are the factors of $x^{9}-x$

So it has 5 factors.