**POLYNOMIALS**

** Class IX NCERT (CBSE) Mathematics **

** NCERT Textbook Exercise 2.1 Solved **

(page 32)

Q1: Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

Answer:

(i) It is a polynomial in one variable* x*.

(ii) This expression is a polynomial in one variable *y*.

(iii) Since exponent of variable *t* in term

which is not a whole number, so this expression is not a polynomial.

(iv) Since the exponent of variable *y* in term

Hence, this expression is not a polynomial.

(v) No it is not a polynomial in one variable. This expression is a polynomial in 3 variables *x*, *y*, and *t*.

Q2: Write the coefficients of x^{2 }in each of the following:

(i) 2 + x^{2 }+ x (ii) 2 – x^{2} + x^{3}

Answer:

(i) The coefficient of x^{2} is 1.

(ii) In this expression, the coefficient of x^{2} is −1.

(iii) Here the coefficient of x^{2} is π/2.

(iv) In the above expression, the coefficient of x^{2} is 0.

Q3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Answer:

By definition, the 'Degree of a Polynomial' is the highest power of the variable in the polynomial.

A binomial has two terms in it. An example of binomial of degree 35 is x^{35} + x^{34}.

A Monomial has only one term in it. An example of monomial of degree 100 is *x*^{100}.

Q4: Write the degree of each of the following polynomials:

Answer:

(i) It is a polynomial in variable *x* and the highest power of variable *x* is 3. Therefore, the degree of this polynomial is 3.

(ii) The given polynomial has variable *y* and the highest power of variable *y* is 2. Therefore, the degree of this polynomial is 2.

(iii) This expression is a polynomial of variable *t* and the highest power of variable *t* is 1. Therefore, the degree of this polynomial is 1.

(iv) Since it is a constant polynomial and the degree of a constant polynomial is always 0.

Q5: Classify the following as linear, quadratic and cubic polynomial:

(i) x^{2} + x (ii) x – x^{3} (iii) y + y^{2} + 4 (iv) 1 + x (v) 3*t*

(vi) *r*^{2} (vii) 7x^{3}

Answer: Linear, quadratic, and cubic polynomials have degrees as 1, 2, and 3 respectively.

(i) This is a quadratic polynomial as its degree is 2.

(ii) This is a cubic polynomial as its degree is 3.

(iii) This is a quadratic polynomial and its degree is 2.

(iv) 1 + *x* is a linear polynomial. Its degree is 1.

(v) *3t *is a linear polynomial. Its degree is 1.

(vi) *r*^{2} is a quadratic polynomial as its degree is 2.

(vii) 7x^{3} is a cubic polynomial and its degree is 3.

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