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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) 4x^{2} – 3x + 7

ii) y^{2} + (sqrt{2})

iii) (3 sqrt{t}+t sqrt{2})

iv) (mathrm{y}+frac{2}{mathrm{y}})

v) x^{10} + y^{3} + t^{50}

Answer:

i) 4x^{2} – 3x + 7

Here polynomial has one variable, i.e. x

ii) y^{2} + (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) x^{10} + y^{3} + t^{50}

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 + x^{2} + x

ii) 2 – x^{2} + x^{3}

iii) (frac{pi}{2})x^{2} + x

v) (sqrt{2} mathrm{x}) – 1

Answer:

i) 2 + x^{2} + x

Here, coefficient of x^{2} is 1.

ii) 2 – x^{2} + x^{3}

Here coefficient of x^{2} is -1

iii) (frac{pi}{2})x^{2} + x

Here coefficient of x^{2} is (frac{pi}{2}).

iv) (sqrt{2} mathrm{x}) – 1

Here coefficint of x^{2} 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) = – x^{35} + 10

ii) A binomial of degree 100

E.g. f(y) = – y^{100}.

Question 4.

Write the degree of each of the following polynomials :

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

ii) 4 – y^{2}

iii) 5t – (sqrt{7})

iv) 3

Answer:

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

ii) 4 – y^{2} 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) x^{2} + x

ii) x – x^{3}

iii) y + y^{2} + 4

iv) 1 + x

iii) 3t

iv) r^{2}

vii) 7x^{3}

Answer:

Linear Polynomial | Quadratic Polynomial | Cubic Polynomial |

iv) 1 + x | i) x^{2} + x | iii) y + y^{2} + 4 |

ii) x – x^{3} | ||

(v) 3t | (vi) r^{2} | (vii) 7x^{3} |

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