Question

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Answer 1

Answer:

The division of p(x)=x3−1 by g(x)=x−1 is as shown above:

Now we know that the division algorithm states that: 

Dividend=(Divisor×quotient)+Remainder

Here, the dividend is x3−1, the divisor is x−1, the quotient is x2+x+1 and the remainder is 0, therefore,

x3−1=[(x−1)(x2+x+1)]+0⇒x3−1=[x(x2+x+1)−1(x2+x+1)]+0⇒x3−1=x3+x2+x−x2−x−1+0⇒x3−1=x3+x2−x2+x−x−1⇒x3−1=x3−1

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Answer 2

Answer:

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