**Telangana SCERT Solution Class IX (9) Math Chapter 2 Polynomials and Factorisation Exercise 2.1**

**(1) (i) x ^{5} – x^{4} + 3**

The highest power of the 3 terms is 5.

So, the degree of the above polynomial is 5.

**(ii) x ^{2} + x – 5**

The highest power of the 3 terms is 2.

∴ The degree of the polynomial is 2.

**(iii) 5**

Now, 5 can be written as 5x^{0} (∵ x^{0} = 1)

∴ The degree of the polynomial is 0.

**(iv) 3x ^{6} + 6y^{3} – 7**

The degree of the polynomial is 6.

**(v) 4 – y ^{2}**

The degree of the polynomial is 2,

**(vi) 5t – ****√3**

The degree of the polynomial is 1.

**(2)** (i) 3x^{2} – 2x + 5 is one variable polynomial since the only variable in the polynomial is x.

(ii) x^{2} + **√**2 is one variable polynomial since the only variable in the polynomial is x.

(iii) P^{2} – 3p + q is a two variable polynomial since there are two variable p and q in the polynomial.

(iv) y + 2/y is a one variable polynomial since there are is only one variable ‘y’ in the polynomial.

(v) 5**√**x + x**√**5 is a one variable polynomial since there is only one variable ‘x’ in the polynomial.

(vi) x^{100} + y^{100} is a two variable polynomial as there are two variables x and y in the polynomial.

**(3) (i) x ^{3} + x + 1**

Coefficient of x^{3} is 1.

**(ii) 2 – x ^{3} + x^{2}**

Coefficient of x^{3} is -1

**(iii) √2x ^{3} + 5**

Coefficient of x^{3} is **√**2

**(iv) 2x ^{3} + 5**

Coefficient of x^{3} is 2.

**(v) π/2 x ^{3} + x**

Coefficient of x^{3} is π/2

**(vi) -2/3 x ^{3}**

Coefficient of x^{3} is -2/3

**(vii) 2x ^{2} + 5 ‘**

or, 2x^{2} + 5 + 0 X x^{3}

Coefficient of x^{3} is 0.

**(viii) 4**

Or, 0 X x^{3} + 4

Coefficient of x^{3} is 4

**(4)** (i) 5x^{2} + x – 7 is a quadratic polynomial having highest degree 2.

(ii) x – x^{3} is a cubic polynomial having highest degree 3.

(iii) x^{2} + x + 4 is a quadratic polynomial having highest degree 2.

(iv) x – 1 is linear polynomial having highest degree 1

(v) 3p is a linear polynomial having highest degree 1.

(vi) πr^{2} is a quadratic polynomial having highest degree 2.

**(5.) (i) A binomial has two terms**

Ans. True.

**(ii) Every polynomial is a binomial**

Ans. False.

**(iii) A binomial may have degree 3**

Ans. True.

**(iv) Degree of zero polynomial is zero**

Ans. False.

**(v) The degree of x ^{2} + 2xy + y^{2} is 2**

Ans. True.

**(vi) πr ^{2} is a monomial**

Ans. True.

**(6)** Monomial of degree 10 is 4x^{10}

Trinomial of degree 10 is 5x^{10} + x^{6} + 3.

Thank you but in 5th bit u should justify