Question

Find the remainder when x^3 - 3x^2 - 3x -1 is divided by x-1 solve by using long division method
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Answer 1

Step-by-step explanation:

Given:-

x^3 - 3x^2 - 3x -1

To find:-

Find the remainder when x^3 - 3x^2 - 3x -1 is divided by x-1 solve by using long division method

Solution:-

See the above attachment

On dividing x^3 - 3x^2 - 3x -1 by x-1 then we get

Quotient = x^2-2x-5

Remainder = -6

Answer:-

Quotient = x^2-2x-5

Remainder = -6

Check:-

We know that

Division Rule:-

Dividend = Divisor×Quotient+Remainder

=> (x-1)(x^2-2x-5)+(-6)

=>x(x^2-2x-5)-1(x^2-2x-5)-6

=>x^3-2x^2-5x-x^2+2x+5-6

=>x^3-3x^2-3x-1

=>Given Polynomial

Verified the given relation.

Used formula:-

Dividend = Divisor×Quotient+Remainder

Answer 2

the remainder is x^2-2x-1