# NCERT Solutions Class 9 Maths Chapter 2 Polynomials

### Exercise 2.1

1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:-
(i) 4x2– 3x + 7
(ii) y2+√2
(iii) 3√t+t√ 2
(iv) y+$\frac{2}{y}$

(v) x10+y3+t50
Sol:- (i) 4x2–3x+7 is a polynomial in one variable. The equation 4x2–3x+7 can be written as 4x2–3x1+7x0 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) y2+2 is a polynomial in one variable. The equation y2+√2 can be written as y2+2y0 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 3t1/2+√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+$\frac{2}{y}$ is not a polynomial in one variable. The equation y+2/y an be written as y+2y-1 though, is the only variable in the given equation, the powers of y (i.e.,-1) is not a whole number.
(v) x10+y3+t50  is not a polynomial in one variable. Here, in the equation x10+y3+t50 though, the powers, 10, 3, 50, are whole numbers, there are 3 variables used in the expression x10+y3+t50.
2. Write the coefficients of x2 in each of the following:
(i) 2+x2+x
(ii) 2-x2+x3
(iii) $\frac{\pi&space;}{2}$x2+x
(iv) √2x-1

Sol:- (i) The coefficient of xin 2+x2+x is 1
(ii) The coefficient of xin 2–x2+xis -1.
(iii) The coefficient of xin $\frac{\pi&space;}{2}$x2+x is $\frac{\pi&space;}{2}$ .
(iv) The coefficient of xin √2x-1 is 0.
3. 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.,  3x35+5.
Monomial of degree 100: A polynomial having one term and the highest degree 100 is called a monomial of degree 100. Eg.,  4x100.
4. Write the degree of each of the following polynomials:
(i) 5x3+4x2+7x
(ii) 4 – y2
(iii) 5t –√7
(iv) 3

Ans:- (i) The degree of 5x3+4x2+7x is 3 as 3 is the highest power of x in the equation.
(ii) The degree of 4–y2 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.
5. Classify the following as linear, quadratic and cubic polynomials:
(i) x2+x
(ii) x-x3
(iii) y+y2+4
(iv) 1+x
(v) 3t
(vi) r2
(vii) 7x3

Sol:- (i) The highest power of x2+x is 2
So, x2+x is a quadratic polynomial.
(ii) The highest power of x–xis 3
So, x–x3 is a cubic polynomial.
(iii) The highest power of y+y2+4 is 2