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.

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.

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’.

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

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.