AP Board 9th Class Maths Solutions Chapter 2 Polynomials and Factorisation Ex 2.1

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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) x5 – x4 + 3
Solution:
Degree is 5.

ii) x2 + x – 5
Solution:
Degree is 2.

iii) 5
Solution:
Degree is 0.

iv) 3x6 + 6y3 – 7
Solution:
Degree is 6.

v) 4 – y2
Solution:
Degree is 2.

vi) 5t – √3
Solution:
Degree is 1.

AP Board 9th Class Maths Solutions Chapter 2 Polynomials and Factorisation Ex 2.1

Question 2.
Which of the following expressions are polynomials in one variable and which are not ? Give reasons for your answer.
i) 3x2 – 2x + 5
Solution:
Given expression is a polynomial in one variable.

ii) x2 + √2
Solution:
Given expression is a polynomial in one variable.

iii) p2 – 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) x100 + y100
Solution:
Given expression has two variables. So it is not a polynomial in one variable.

AP Board 9th Class Maths Solutions Chapter 2 Polynomials and Factorisation Ex 2.1

Question 3.
Write the coefficient of x3 in each of the following.
i) x3 + x + 1
ii) 2 – x3+ x2
iii) \(\sqrt{2} x^{3}+5\)
iv) 2x3 + 5
v) \(\frac{\pi}{2} x^{3}+x\)
vi) \(-\frac{2}{3} x^{3}\)
vii) 2x2 + 5
viii) 4
Solution:
i) x3 + x + 1 : co-efficient of x3 is 1.
ii) 2 – x3+ x2 : co-efficient of x3 is – 1.
iii) \(\sqrt{2} x^{3}+5\) co-efficient of x3 is √2
iv) 2x3 + 5 : co-efficient of x3 is 2.
v) \(\frac{\pi}{2} x^{3}+x\) co-efficient of x3 is \(\frac{\pi}{2}\)
vi) \(-\frac{2}{3} x^{3}\) co-efficient of x3 is \(-\frac{2}{3}\)
vii) 2x2 + 5 : co-efficient of x3 is ‘0’.
viii) 4 : co-efficient of x3 is ‘0’.

AP Board 9th Class Maths Solutions Chapter 2 Polynomials and Factorisation Ex 2.1

Question 4.
Classify the following as linear, quadratic and cubic polynomials.
i) 5x2+ x – 7 : degree 2 hence quadratic polynomial.
ii) x – x3 , : degree 3 hence cubic polynomial.
iii) x2 + x + 4 : degree 2 hence quadratic polynomial.
iv) x – 1 : degree 1 hence linear polynomial.
v) 3p : degree 1 hence linear polynomial.
vi) πr2 : 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 x2 + 2xy + y2 is 2
vi) πr2 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 x2 + 2xy + y2 is 2 – True
vi) πr2 is monomial – True

AP Board 9th Class Maths Solutions Chapter 2 Polynomials and Factorisation Ex 2.1

Question 6.
Give one example each of a monomial and trinomial of degree 10.
Solution :
– 7x10 is a monomial of degree 10.
3x2y8 + 7xy – 8 is a trinomial of degree 10.