AP State Syllabus AP Board 9th Class Maths Solutions Chapter 2 Polynomials and Factorisation Ex 2.1 Textbook Questions and Answers.

## AP State Syllabus 9th Class Maths Solutions 2nd Lesson Polynomials and Factorisation Exercise 2.1

Question 1.

Find the degree of each of the polynomials given below,

i) x^{5} – x^{4} + 3

Solution:

Degree is 5.

ii) x^{2} + x – 5

Solution:

Degree is 2.

iii) 5

Solution:

Degree is 0.

iv) 3x^{6} + 6y^{3} – 7

Solution:

Degree is 6.

v) 4 – y^{2}

Solution:

Degree is 2.

vi) 5t – √3

Solution:

Degree is 1.

Question 2.

Which of the following expressions are polynomials in one variable and which are not ? Give reasons for your answer.

i) 3x^{2} – 2x + 5

Solution:

Given expression is a polynomial in one variable.

ii) x^{2} + √2

Solution:

Given expression is a polynomial in one variable.

iii) p^{2} – 3p + q

Solution:

Given expression is not a polynomial in one variable. It involves two variables p and q.

iv) y + \(\frac{2}{\mathbf{y}}\)

Solution:

Given expression is not a polynomial. Since the second term contains the variable in its denominator.

v) \(5 \sqrt{x}+x \sqrt{5}\)

Solution:

Given expression is not a polynomial. Since the first term’s exponent is not an integer.

vi) x^{100} + y^{100}

Solution:

Given expression has two variables. So it is not a polynomial in one variable.

Question 3.

Write the coefficient of x^{3} in each of the following.

i) x^{3} + x + 1

ii) 2 – x^{3}+ x^{2}

iii) \(\sqrt{2} x^{3}+5\)

iv) 2x^{3} + 5

v) \(\frac{\pi}{2} x^{3}+x\)

vi) \(-\frac{2}{3} x^{3}\)

vii) 2x^{2} + 5

viii) 4

Solution:

i) x^{3} + x + 1 : co-efficient of x^{3} is 1.

ii) 2 – x^{3}+ x^{2} : co-efficient of x^{3} is – 1.

iii) \(\sqrt{2} x^{3}+5\) co-efficient of x^{3} is √2

iv) 2x^{3} + 5 : co-efficient of x^{3} is 2.

v) \(\frac{\pi}{2} x^{3}+x\) co-efficient of x^{3} is \(\frac{\pi}{2}\)

vi) \(-\frac{2}{3} x^{3}\) co-efficient of x^{3} is \(-\frac{2}{3}\)

vii) 2x^{2} + 5 : co-efficient of x^{3} is ‘0’.

viii) 4 : co-efficient of x^{3} is ‘0’.

Question 4.

Classify the following as linear, quadratic and cubic polynomials.

i) 5x^{2}+ x – 7 : degree 2 hence quadratic polynomial.

ii) x – x^{3} , : degree 3 hence cubic polynomial.

iii) x^{2} + x + 4 : degree 2 hence quadratic polynomial.

iv) x – 1 : degree 1 hence linear polynomial.

v) 3p : degree 1 hence linear polynomial.

vi) πr^{2} : degree 2 hence quadratic polynomial.

Question 5.

Write whether the following statements are True or False. Justify your answer.

i) A binomial can have at the most two terms

ii) Every polynomial is a binomial

iii) A binomial may have degree 3

iv) Degree of zero polynomial is zero

v) The degree of x^{2} + 2xy + y^{2} is 2

vi) πr^{2} is monomial

Solution :

i) A binomial can have at the most two terms -True

ii) Every polynomial is a binomial – False

[∵ A polynomial can have more than two terms]

iii) A binomial may have degree 3 – True

iv) Degree of zero polynomial is zero – False

v) The degree of x^{2} + 2xy + y^{2} is 2 – True

vi) πr^{2} is monomial – True

Question 6.

Give one example each of a monomial and trinomial of degree 10.

Solution :

– 7x^{10} is a monomial of degree 10.

3x^{2}y^{8} + 7xy – 8 is a trinomial of degree 10.