# NCERT Solutions Class 9 Maths Chapter 2 Polynomials

### Exercise 2.1

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

(i) 4x^{2}– 3x + 7

(ii) y^{2}+√2

(iii) 3√t+t√ 2

(iv) y+**(v) x**^{10}+y^{3}+t^{50}**Sol:-**(i) 4x^{2}–3x+7 is a polynomial in one variable. The equation 4x^{2}–3x+7 can be written as 4x^{2}–3x^{1}+7x^{0}and since*x*is the only variable in the given equation and the powers of x (i.e., 2, 1 and 0) are whole numbers.

(ii) y^{2}+**√**2 is a polynomial in one variable. The equation y^{2}+**√2**can be written as y^{2}+**√**2y^{0}Since y is the only variable in the given equation and the powers of y (i.e., 2 and 0) are whole numbers.

(iii) 3√t+t√2 is not a polynomial in one variable. The equation 3√t+t√2 can be written as 3t^{1/2}+√2t though,*t*is the only variable in the given equation, the powers of*t*(i.e.,1/2) is not a whole number.

(iv) y**+**is not a polynomial in one variable. The equation y+2/y an be written as y+2y^{-1}though,*y*is the only variable in the given equation, the powers of*y*(i.e.,-1) is not a whole number.

(v) x^{10}+y^{3}+t^{50}is not a polynomial in one variable. Here, in the equation x^{10}+y^{3}+t^{50}though, the powers, 10, 3, 50, are whole numbers, there are 3 variables used in the expression x^{10}+y^{3}+t^{50}.**Write the coefficients of x**^{2}in each of the following:**(i) 2+x**^{2}+x

(ii) 2-x^{2}+x^{3}

(iii) x^{2}+x

(iv) √2x-1**Sol:-**(i) The coefficient of x^{2 }in 2+x^{2}+x is 1

(ii) The coefficient of x^{2 }in 2–x^{2}+x^{3 }is -1.

(iii) The coefficient of x^{2 }in x^{2}+x is .

(iv) The coefficient of x^{2 }in √2x-1 is 0.**Give one example each of a binomial of degree 35, and of a monomial of degree 100.****Sol:-**Binomial of degree 35: A polynomial having two terms and the highest degree 35 is called a binomial of degree 35. Eg., 3x^{35}+5.

Monomial of degree 100: A polynomial having one term and the highest degree 100 is called a monomial of degree 100. Eg., 4x^{100}.**Write the degree of each of the following polynomials:**

(i) 5x^{3}+4x^{2}+7x

(ii) 4 – y^{2}

(iii) 5t –√7

(iv) 3**Ans:-**(i) The degree of 5x^{3}+4x^{2}+7x is 3 as 3 is the highest power of x in the equation.

(ii) The degree of 4–y^{2}is 2 as 2 is the highest power of y in the equation.

(iii) The degree of 5t**–√7**is 1 as 1 is the highest power of y in the equation.

(iv) The degree of 3 is 0.**Classify the following as linear, quadratic and cubic polynomials:**

(i) x^{2}+x

(ii) x-x^{3}

(iii) y+y^{2}+4

(iv) 1+x

(v) 3t

(vi) r^{2}

(vii) 7x^{3}**Sol:-**(i) The highest power of x^{2}+x is 2

So, x^{2}+x is a quadratic polynomial.

(ii) The highest power of x–x^{3 }is 3

So, x–x^{3}is a cubic polynomial.

(iii) The highest power of y+y^{2}+4 is 2

So, y+y^{2}+4is a quadratic polynomial.

(iv) The highest power of 1+x is 1

So, 1+x is a linear polynomial.

(v) The highest power of 3t is 1

So, 3t is a linear polynomial.

(vi) The highest power of r^{2 }is 2

So, r^{2}is a quadratic polynomial.

(vii) The highest power of 7x^{3 }is 3

So, 7x^{3}is a cubic polynomial.

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