KSEEB Solutions for Class 9 Maths Chapter 4 Polynomials Ex 4.1

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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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:

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