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 \(x^4+10x^3+100x^2+1000x+1000\)
