Question

If the polynomial x^5 − 10^5 can be split as the product of the polynomials

x − 10 and a, what is a?

Answer 1

Hello,

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

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

Explanation:

Given :
`x^5 − 10^5`

To Find: If the polynomial
`x^5 − 10^5` can be split as the product of the polynomials x − 10 and a, what is a?

Solution:

`(x-10)(a)=x^5 − 10^5`

`a=(x^5 − 10^5)/(x-10)`

Since we know that:

`Dividend = (Divisor * Quotient)+Remainder`

`x^5 -10^5= (x-10 * x^4)+(10x^4-10^5)`

`x^5-10^5= (x-10 * x^4+10x^3)+(100x^3-10^5)`

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

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

`x^5-10^5= (x-10 * x^4+10x^3+100x^2+1000x+1000)+0`

So, a =
`x^4+10x^3+100x^2+1000x+1000`

Hence the value of a is
`x^4+10x^3+100x^2+1000x+1000`