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

Answer:

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

Step-by-step 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:

$(x-10)(a)=x^5 − 10^5$

$a=\frac{x^5 − 10^5}{x-10}$

Since we know that:

$Dividend = (Divisor \times Quotient)+Remainder$

$x^5 -10^5= (x-10 \times x^4)+(10x^4-10^5)$

$x^5-10^5= (x-10 \times x^4+10x^3)+(100x^3-10^5)$

$x^5-10^5= (x-10 \times x^4+10x^3+100x^2)+(1000x^2-10^5)$

$x^5-10^5= (x-10 \times x^4+10x^3+100x^2+1000x)+(10000x-10^5)$

$x^5-10^5= (x-10 \times x^4+10x^3+100x^2+1000x+1000)+0$

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

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