##### Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm:(i) (ii)(iii)

(i) and

Degree of ; therefore degree of and degree of remainder is of degree 1 or less,

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

Since remainder is zero, therefore

(ii) and

Degree of ; therefore degree of and degree of remainder is of degree 1 or less,

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

Since remainder is 2, therefore

(iii) and

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

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

Since remainder is , therefore

2