Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in each of the following:

(i)

(ii)

(iii)

(iv)

(i) and

Degree of ; therefore degree of and degree of remainder is less than 2,

Let and

By applying division algorithm:

Dividend = Quotient× Divisor + Remainder

On substituting values in the above relation we get,

On comparing coefficients we get,

On solving above equations we get,

, , ,

On substituting these values for

(ii) and

Degree of ; therefore degree of and degree of remainder is less than 2.

Let and

By applying division algorithm:

Dividend = Quotient× Divisor + Remainder

On substituting values in the above relation we get,

On comparing coefficients we get,

On solving above equations we get,

, , , ;

On substituting these values for

(iii) and

Degree of ; therefore degree of and degree of remainder is less than 2,

Let and

By applying division algorithm:

Dividend = Quotient× Divisor + Remainder

On substituting values in the above relation we get,

On comparing coefficients we get,

On solving above equations we get,

, , ,

On substituting these values for

(iv) and

Degree of ; therefore degree of and degree of remainder is less than 2,

Let and

By applying division algorithm:

Dividend = Quotient× Divisor + Remainder

On substituting values in the above relation we get,

On comparing coefficients we get,

On solving above equations we get,

, , ,

On substituting these values for

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