Question

by actual division find the quotient and the remainder when the first polynomial divided by the second polynomial
x^4+1;x-1​

Answer 1

Here's your answer...hope it helps!!

Answer 2

Here ,

We need to divide x⁴ + 1 by (x - 1) .

_______

x - 1 ) x⁴ + 1 ( x³ + x² + x +1

x⁴ - x³

– +

____________

x³ + 1

x³ –x²

_ +

____________

x² – 1

x² -x

– +

____________

x+1

x– 1

- +

___________

2

____________

Clearly ,

Dividend = x⁴ + 1

Divisor = x - 1

Quotient = x³ + x² + x +1

Remainder = 2

Also ,

We know that ,

Dividend = Divisor•Quotient + Remainder

Thus ,

x⁴ + 1 = x - 1•x³ + x² + x +1+2

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