# If the polynomial x5 − 105 can be split as the product of the polynomials x − 10 and a, what is a?

If the polynomial x5 − 105 can be divided as the product of the polynomials x − 10 and a, what is a? x4 − 99990 x4 + 10×3 + 100×2 + 1000x − 10000 x4 + 10×3 + 100×2 + 1000x + 10000

Answer 1

X^4+10x^3+100x^2+1000x+10000

answer 2

Walkthrough: Here the given polynomial, Since, it can be divided as the product of the polynomials x – 10 and a, Then we can write, By long division (shown below), we get,

answer 3

The value of a is: Walkthrough: we know that: Here, a=10 and n=5 ⇒ So the value of a is:

answer 4

using synthetic division,

Answer 5

The mathematical expression that can be used to correctly express the given scenario is, x⁵ – 10⁵ = (x – 10)(a) The value of a, as shown above, can be calculated by the equation, a = ( x⁵ – 10⁵) / (x – 10) There are two ways to solve the problem: synthetic division and the long path. Each of them will produce the same response. Simplifying the value of a will give us a final answer of, a = x⁴ + 10x³ + 100x² + 1000x