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

Answer:

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

Step-by-step 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,

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

$\implies a = \frac{x^5-10^5}{x-10}$

By the long division ( shown below ),

We get,

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