KSEEB Solutions for Class 9 Maths Chapter 4 Polynomials Ex 4.1 are part of KSEEB Solutions for Class 9 Maths. Here we have given Karnataka Board Class 9 Maths Chapter 4 Polynomials Exercise 4.1.

## Karnataka Board Class 9 Maths Chapter 4 Polynomials Exercise 4.1

Question 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 + $$\sqrt{2}$$
iii) $$3 \sqrt{t}+t \sqrt{2}$$
iv) $$\mathrm{y}+\frac{2}{\mathrm{y}}$$
v) x10 + y3 + t50
i) 4x2 – 3x + 7
Here polynomial has one variable, i.e. x
ii) y2 + $$\sqrt{2}$$
Here polynomial has one variable, i.e. y
iii) $$3 \sqrt{t}+t \sqrt{2}$$
This is polynmomial with one variable, because T is only one variable.
iv) $$\mathrm{y}+\frac{2}{\mathrm{y}}$$
Here polynomial has one variable, ie. y.
v) x10 + y3 + t50
This polynomial is not having one variable because here 3 variables means ‘x’, y and ‘t’ are there.

Question 2.
Write the coefficients of x in each of the followng :
i) 2 + x2 + x
ii) 2 – x2 + x3
iii) $$\frac{\pi}{2}$$x2 + x
v) $$\sqrt{2} \mathrm{x}$$ – 1
i) 2 + x2 + x
Here, coefficient of x2 is 1.
ii) 2 – x2 + x3
Here coefficient of x2 is -1
iii) $$\frac{\pi}{2}$$x2 + x
Here coefficient of x2 is $$\frac{\pi}{2}$$.
iv) $$\sqrt{2} \mathrm{x}$$ – 1
Here coefficint of x2 is -1.

Question 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100
i) A Bionomial of degree 35
E.g. f(x) = – x35 + 10
ii) A binomial of degree 100
E.g. f(y) = – y100.

Question 4.
Write the degree of each of the following polynomials :
i) 5x3 + 4x2 + 7x
ii) 4 – y2
iii) 5t – $$\sqrt{7}$$
iv) 3
i) 5x3 + 4x2 + 7x Highest power (degree) 3
ii) 4 – y2 Highest power degree) 2
iii) 5t – $$\sqrt{7}$$ Highest power (degree) 1
iv) 3 Highest power (degree) 0

Question 5.
Classify the folloiwng as linear, quadratic and cubic polynomials :
i) x2 + x
ii) x – x3
iii) y + y2 + 4
iv) 1 + x
iii) 3t
iv) r2
vii) 7x3