27 Jun, 2021 02:19 PM

Can you solve this polynomial long division question?

See if you can figure this one out. Use polynomial long division to evaluate (x^2-1)/(x-1) , (x^3-1)/(x-1) , and (x^4-1)/(x-1). Then with these results try and write down a general formula for ( x^n-1)/(x-n). Where n is any Natural Number. ( There is a hint: look at the way the definition of "polynomial" is written.)

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Answer
CO
27 Jun, 2021 02:19 PM

1. (x+1)
2. (x²+x+1)
3. (x³+x²+x+1)

General formula: (x^n - 1)/(x - 1) = (x^(n-1) + x^(n-2) + x^(n-3) + .....+ x^(n-n)