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**Q1. Which of the following expressions are polynomials in one variable and which are not?**

**1. 3x ^{2}–4x+15 2. y^{2}+2√3 3. 3√x+√2x 4. 5. x^{12}+y^{2}+t^{50}**

**Sol :**

1. **3x ^{2}–4x+15** – it is a polynomial of x

2. **y ^{2}+2√3** – it is a polynomial of y

3. **3√x+√2x** – it is not a polynomial since the exponent of 3√x is not a positive term

4. it is not a polynomial since the exponent of is not a positive term

5. x^{12}+y^{2}+t^{50} – it is a three variable polynomial which variables of x, y, t

**Q2. Write the coefficients of x ^{2} in each of the following**

**Sol :**

Given , to find the coefficients of x^{2}

1. 17–2x+7x^{2} – the coefficient is 7

2. 9–12x+x^{2} – the coefficient is 0

3. the coefficient is

4. the coefficient is 0

**Q3. Write the degrees of each of the following polynomials :**

**1. 7x ^{3}+4x^{2}–3x+12**

2. 12–x+2x^{2}

3. 5y–√2

4. 7−7x^{0}

5. 0

**Sol :**

Given , to find degrees of the polynomials

Degree is highest power in the polynomial

1. 7x3+4x^{2}–3x+12 – the degree is 3

2. 12–x+2x^{3} – the degree is 3

3. 5y–√2 – the degree is 1

4. 7−7x^{0} – the degree is 0

5. 0 – the degree of 0 is not defined

**Q4. Classify the following polynomials as linear, quadratic, cuboc and biquadratic polynomials :**

**1. x+x ^{2}+4 2. 3x – 2 3. 2x+x^{2} 4. 3y 5. t^{2}+1**

**f . 7t ^{4}+4t^{2}+3t–2**

**Sol :**

Given

1. x+x^{2}+4 – it is a quadratic polynomial as its degree is 2

2. 3x – 2 – it is a linear polynomial as its degree is 1

3. 2x+x^{2} – it is a quadratic polynomial as its degree is 2

4. 3y – it is a linear polynomial as its degree is 1

5. t^{2}+1 – it is a quadratic polynomial as its degree is 2

f . 7t^{4}+4t^{2}+3t–2 – it is a bi- quadratic polynomial as its degree is 4

**Q5. Classify the following polynomials as polynomials in one variables, two – variables etc :**

**1. x ^{2}–xy+7y^{2}**

2. x^{2}–2tx+7t^{2}–x+t

3. t^{3}–3t^{2}+4t–5

4. xy + yz + zx

**Sol :**

Given

1. x^{2}–xy+7y^{2} – it is a polynomial in two variables x and y

2. x^{2}–2tx+7t^{2}–x+t – it is a polynomial in two variables x and t

3. t^{3}–3t^{2}+4t–5– it is a polynomial in one variable t

4. xy+yz+zx – it is a polynomial in 3 variables in x , y and z

**Q6. Identify the polynomials in the following :**

**Sol :**

Given

1. f(x) = 4x^{3}–x^{2}−3x+7 – it is a polynomial

2. b. g(x) = 2x^{3}–3x^{2}+√x–1 – it is not a polynomial since the exponent of √x is a negative integer

3. it is a polynomial as it has positive integers as exponents

4. it is not a polynomial since the exponent of 4/x is a negative integer

5. it is not a polynomial since the exponent of is a negative integer

6. it is not a polynomial since the exponent of 3/x is a negative integer

**Q7. Identify constant , linear , quadratic abd cubic polynomial from the following polynomials :**

1. f(x) = 0

2. g(x) = 2x^{3}–7x+4

3.

4. p(x) = 2x^{2}–x+4

5. q(x) = 4x+3

6. r(x) = 3x^{3}+4x^{2}+5x–7

**Sol :**

Given ,

1. f(x) = 0 – as 0 is constant , it is a constant variable

2. g(x) = 2x^{3}–7x+4 – since the degree is 3 , it is a cubic polynomial

3. – since the degree is 1 , it is a linear polynomial

4. p(x) = 2x^{2}–x+4 – since the degree is 2 , it is a quadratic polynomial

5. q(x) = 4x+3 – since the degree is 1 , it is a linear polynomial

6. r(x) = 3x^{3}+4x^{2}+5x–7 – since the degree is 3 , it is a cubic polynomial

**Q8. Give one example each of a binomial of degree 25, and of a monomial of degree 100**

**Sol :**

Given , to write the examples for binomial and monomial with the given degrees

Example of a binomial with degree 25 – 7x^{35–}5

Example of a monomial with degree 100 – 2t^{100}

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