A mathematical expression containing variables, coefficients along with integer exponents, which are not negative is called Polynomial. Polynomial equations are primarily used to describe polynomial functions and are primarily used in areas of mathematics and science. The different fields that polynomials are used for are:

- Physics
- Chemistry
- Social Science
- Economics
- Calculus
- Numerical Analysis
- Algebraic Geometry

The different types of Polynomials are:

- Matrix Polynomials
- Trigonometric Polynomials
- Rational Functions
- Laurent Polynomials
- Power Series

Learn more about RS Aggarwal Class 9 Solutions Chapter 2 Polynomials below:

**Question 1: **

**Which of the following expressions are polynomials?**

**(i) x ^{5 }-2x^{3} + x+7**

It is a polynomial, Degree = 5.

(ii**) y ^{3 }– 3–√y**

It is polynomial, Degree = 3.

**(iii) t ^{2}–25t+2–√**

It is polynomial, Degree = 2.

**(iv) 5z√−6**

It is not a polynomial.

**(v) x−1x**

It is not a polynomial.

**(vi) x108−1**

It is polynomial, Degree = 108.

**(vii) x−−√3−27**

It is not a polynomial.

**(viii) 12√x2−2–√x+2**

It is a polynomial, Degree = 2.

**(ix) x−2+2x−1+3**

It is not a polynomial.

**(x) 1**

It is a polynomial, Degree = 0.

**(xi) –35**

It is a polynomial, Degree = 0.

**(xii) 2–√3y2−8**

It is a polynomial, Degree = 2.

**Question 2:**

**Write the degree of each of the following polynomials:**

The degree of a polynomial in one variable is the highest power of the variable.

**(i)2x-5–√**

Degree of 2x – 5–√ is 1.

**(ii) 3 – x + x ^{2}-6x^{3}**

Degree of 3 – x + x^{2}– 6x^{3} is 3.

**(iii)9**

Degree of 9 is 0.

**(iv) 8x ^{4}-36x+5x^{7}**

Degree of 8x^{4} – 36x + 5x^{7} is 7.

**(v)x ^{9}-x^{5}+3x^{10}+8**

Degree of x^{9} – x^{5} 3x^{10} + 8 is 10.

**(vi) 2-3x ^{2}**

Degree of 2 – 3x^{2} is 2.

**Question 3:**

**Write :**

**(i) Coefficient of x ^{3} in 2x + x^{2} – 5x^{3}+ x^{4}**

-5

**(ii)** **Coefficient of x in 3–√ – 22x−−√ + 4x ^{2}**

— 22–√

**(iii) Coefficient of x ^{2} in ∏÷3 x^{2} + 7x-3**

∏÷3

**(iv)** ** Coefficient of x ^{2} in 3x – 5**

0.

**Question 4: **

**(i)** **Give an example of a binomial of degree 27.**

x^{27} — 36

**(ii) Give an example of a monomial of degree 16.**

y1^{16}

**(iii) Give an example of a trinomial of degree 3.**

5x^{3} — 8x + 7

**Question 5: **

**Classify the following as linear, quadratic and cubic polynomials :**

**(i)** **2x ^{2 }+ 4x**

It is a quadratic polynomial.

**(ii)** **x – x ^{3}**

It is a cubic polynomial.

**(iii)** **2 – y – y ^{2}**

It is a quadratic polynomial.

**(iv)** **-7 + z**

It is a linear polynomial.

**(v) 5t**

It is a linear polynomial.

**(vi**) ^{ } **p ^{3 } **

It is a cubic polynomial.

**Question 6**:

**If p(x) = 5 – 4x + 2x ^{2}, find**

**(i)** **p(0)**

= 5 – 4(0) + 2(0)^{2}

= 5

**(ii)** **p(3)**

= 5 – 4(3) + 2(3)^{2}

= 5 – 12 + 18

= 23 – 12

= 11

**(iii) p(-2)**

= 5 – 4(-2) + 2(-2)^{2}

= 5 + 8 + 8

= 21

**Question 7:**

**If P(Y) = 4 + 3Y – Y ^{2}+ 5y^{3 }, find**

**(i) p(0)**

= 4 + 3(0) – 0^{2} + 5(0)^{3}

= 4 + 0 – 0 + 0

= 4

**(ii) p(2)**

= 4 + 3(2) – 2^{2} + 5(2)^{3}

= 4 + 6 – 4 + 40

= 10 – 4 + 40

= 46

**(III) p(-1) **

= 4 + 3(-1) – (-1)2 + 5(-1)^{3}

= 4 – 3 – 1 – 5

= -5

**Question 8**:

**If f(t) = 4t ^{2} – 3t + 6, find **

**(i) f(0)**

= 4(0)^{2} – 3(0) + 6

= 0 – 0 + 6

= 6

**(ii) f(4)**

= 4(4)^{2} – 3(4) + 6

= 64 – 12 + 6

= 58

**(iii) f(-5)**

= 4(-5)^{2} – 3(-5) + 6

= 100 + 15 + 6

= 121