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NCERT Class 10 Mathematics Solutions: Chapter 2- Polynomials Exercise 2.3 Part 4

Illustration: NCERT Class 10 Mathematics Solutions: Chapter 2- Polynomials Exercise 2.3 Part 4

1. Give examples of polynomial which satisfy the division algorithm and

(i)

(ii)

(iii)

Answer:

According to the division algorithm, if are two polynomials with

Then we can find polynomials such that

Where or degree of degree of

Degree of quotient will be equal to degree of dividend when divisor is constant.

(i) Now assume the division of by

Degree of is same i.e.. , 2.

Checking for division algorithm,

Or,

Hence, division algorithm is satisfied.

(ii) Assume the division of

Clearly, the degree of is the same i.e.. , 1

Checking for division algorithm

So, the division algorithm is satisfied.

(iii) Assume the division of by

Clearly, the degree of is 0.

Checking for division algorithm,

Thus, the division algorithm is satisfied.