Show that 5x7-7x5+2 is exactly divisible by (x-1)² and find the quotient.

let f(x)=5x^7-7x^5+2

clearly f(1)=0 and f`(1)=0

So 1 is a double root of f(x).

now knowing that (x-1)^2 is a factor of f(x) you can find the quotient by using simple division