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

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

Answer 2

`x^4 + 10x^3 + 100x^2 + 1,000x + 10,000`

Explanation:

Here, the given polynomial,

`x^5-10^5`

Since, it can be split as the product of the polynomials x − 10 and a,

So, we can write,

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

`\implies a = (x^5-10^5)/(x-10)`

By the long division ( shown below ),

We get,

`a=x^4 + 10x^3 + 100x^2 + 1,000x + 10,000`