Answer :

Given, x3 – 1, x – 1 as pair of polynomials


Need to find the quotient and remainder


To find the quotient and remainder the given equation can be written as p(x) = (x – a)q(x) + b


since, the polynomial is of third degree we can write the q(x) as x2 + ax + b


p(x) = (x – a)( x2 + ax + b) + c


x3 – 1 = (x – 1)( x2 + ax + b) + c


x3 – 1 = (x3 –x2 + ax2 – ax + bx – b) + c


x3 – 1 = x3 + (a–1)x2 + (b – a)x + (c – b)


a – 1 = 0, b – a = 0, c – b = – 1


a = 1, b = 1


c = b – 1 = 0


Quotient = x2 + ax + b = x2 + x + 1


Remainder = 0


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