Question

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

Answer 1

Hello,

using synthetic division,

`x^5-10^5=(x-10)(x^4+10x^3+100x^2+1000x+10000).`

Answer 2

Value of a is:

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

Explanation:

we know that:

`x^n-a^n=(x-a)(x^(n-1)+ax^(n-2)+a^2x^(n-3)+...+a^(n-2)x+a^(n-1))`

Here, a=10 and n=5

`x^5-10^5=(x-10)(x^4+10x^3+100x^2+1000x+10000)`

`x^5-10^5=(x-10)a`

⇒
`a=x^4+10x^3+100x^2+1000x+10000`

Hence,Value of a is:

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