Can you explain how we found the answer here please How many

How many ways to represent p(x) = (x^2 - 1) (x^2 - 4) (x^2 - 9)(x^2 - 16)(x^2 - 25) as a product of 2 polynomials of degree S with leading coefficient of (x) = (x - 1)(x + 1)(x - 2)(x + 2)(x - 3)(x + 3)(y - 4)(y + 4)(x - 5)(x + 5) 1/2 (10 5)

Solution

There are 10 terms: (x+1), (x-1), (x+2), (x-2), (x+3), (x-3), (x+4), (x-4), (x+5) and (x-5).

Since we are looking to form a polynomial of degree 5, we need to pick five of these term from 10 which can be done in ¹⁰C₅ ways.