# Bihar Board Class 9th Maths Solutions Chapter 2 Polynomials Ex 2.1

Bihar Board Class 9th Maths Solutions Chapter 2 Polynomials Ex 2.1 Textbook Questions and Answers.

## BSEB Bihar Board Class 9th Maths Solutions Chapter 2 Polynomials Ex 2.1

Question 1.
Which of the following expressions are polynomials in one variable and which are not ? State reasons for- your answer.

1. 4x² – 3x + 7
2. y² + $$\sqrt{2}$$
3. 3$$\sqrt{t}$$ + t$$\sqrt{2}$$
4. y + $$\frac { 2 }{ y }$$
5. x10 + y³ + t50

Solution:

1. In 4x² – 3x + 7, all the indices of x are whole numbers so it is a polynomial in one variable x.
2. In y² + $$\sqrt{2}$$ the index of y is a whole number so it is a polynomial in one variable y.
3. 3$$\sqrt{t}$$ + t$$\sqrt{2}$$ = 3t$$\frac { 2 }{ y }$$ + $$\sqrt{2}$$t, here the exponent of the first term is $$\frac { 1 }{ 2 }$$, which is not a whole number. Therefore, it is not a polynomial.
4. y + $$\frac { 2 }{ y }$$ = y + 2y-1 here the exponent of the second term is – 1, which is not a whole number and so it is not a polynomial.
5. x10 + y³ + t50 is not a polynomial in one variable as three variables x, y, t occur in it.

Question 2.
Write the coefficients. of x² in each of the following:

1. 2 + x² + x
2. 2 – x³ + x³
3. $$\frac { π }{ 2 }$$ x² + x
4. $$\sqrt{2}$$x – 1

Solution:
Coefficient of x² :

1. in 2 + x² + x is 1
2. in 2 – x² + x³ is – 1
3. in $$\frac { π }{ 2 }$$ x² + x $$\frac { π }{ 2 }$$
4. in $$\sqrt{2x}$$ – 1 is 0.

Question 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:

1. Binomial of degree 35 may be taken as x35 + 4x
2. Monomial of degree 100 may be taken as 5x100.

Question 4.
Write the degree of each of the following polynomials :
Solution:

1. The highest power term is 5x³ and the exponent is 3. So, the degree is 3.
2. The highest power term is – y² and the exponent is 2. So, the degree is 2.
3. The highest power term is 51 and the exponent is 1. So, the degree is 1.
4. The only term here is 3 which can be written as 3x° and so the exponent is 0. Therefore, the degree is 0.

Question 5.
Classify the following as linear, quadratic and cubic polynomials :

1. x² + x
2. x – x³
3. y + y² + 4
4. 1 + x
5. 3t
6. 7x³

Solution:

1. The highest degree of x² + x is 2, so it is a quadratic.
2. The highest degree of x – x³ is 3, so it is a cubic.
3. The highest degree of y + y² + 4 is 2, so it is a quadratic.
4. The highest degree of x in 1 + x in 1. So it is a linear polynomial.
5. The highest degree of t in 3t is 1. So it is a linear polynomial.
6. The highest degree of r in r² is 2. So, it is a quadratic polynomial.
7. The highest degree of x in 7x³ is 3. So, it is cubic polynomial.