Question

If the polynomial x5 − 105 can be split as the product of the polynomials
x − 10 and a, what is a?
x4 − 99,990
x4 + 10x3 + 100x2 + 1,000x − 10,000
x4 + 10x3 + 100x2 + 1,000x + 10,000

Answer 1

the multiplication of \(a\) with \((x-10)\) must give \((x^5-105)\) as product

so

\(a \times (x-10)=x^5-105\)

\(a=\large \frac{x^5-105}{x-10}\)

do this division to get your solution! :)