Q. 2 D5.0( 1 Vote )

# For each pair of

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

c = 0

Quotient = x2 + ax + b = x2 – x + 1

Remainder = 0

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