RS Aggarwal Solutions Class 9 Polynomials

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:

  1. Matrix Polynomials
  2. Trigonometric Polynomials
  3. Rational Functions
  4. Laurent Polynomials
  5. Power Series

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

Question 1:

Which of the following expressions are polynomials?

(i) x5 -2x3 + x+7

It is a polynomial, Degree = 5.

(ii) y3 3y

It is polynomial, Degree = 3.

(iii) t225t+2

It is polynomial, Degree = 2.

(iv) 5z6

It is not a polynomial.

(v) x1x

It is not a polynomial.

(vi) x1081

It is polynomial, Degree = 108.

(vii) x327

It is not a polynomial.

(viii) 12x22x+2

It is a polynomial, Degree = 2.

(ix) x2+2x1+3

It is not a polynomial.

(x) 1

It is a polynomial, Degree = 0.

(xi) –35

It is a polynomial, Degree = 0.

(xii) 23y28

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 + x2-6x3

Degree of 3 – x + x2– 6x3 is 3.

(iii)9

Degree of 9 is 0.

(iv) 8x4-36x+5x7

Degree of 8x4 – 36x + 5x7 is 7.

(v)x9-x5+3x10+8

Degree of x9 – x5 3x10 + 8 is 10.

(vi) 2-3x2

Degree of 2 – 3x2 is 2.

Question 3:

Write :

(i) Coefficient of x3 in 2x + x2 – 5x3+ x4

-5

(ii) Coefficient of x in 3 – 22x + 4x2

— 22

(iii) Coefficient of x2 in ÷3 x2 + 7x-3

÷3

(iv)   Coefficient of x2 in 3x – 5

0.

Question 4:

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

x27 — 36

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

y116

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

5x3 — 8x + 7

Question 5:

Classify the following as linear, quadratic and cubic polynomials :

(i)               2x2 + 4x

It is a quadratic polynomial.

(ii)         x – x3

It is a cubic polynomial.

(iii)       2 – y – y2

It is a quadratic polynomial.

(iv)   -7 + z

It is a linear polynomial.

(v)     5t

It is a linear polynomial.

(vi)    p3  

It is a cubic polynomial.

 

Question 6:

If p(x) = 5 – 4x + 2x2, 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 – Y2+ 5y3 , find

(i) p(0)

= 4 + 3(0) – 02 + 5(0)3

= 4 + 0 – 0 + 0

= 4

(ii) p(2)

= 4 + 3(2) – 22 + 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) = 4t2 – 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


Practise This Question

Fractional distillation is the separation of a mixture into its component parts or fractions. This is the process of separation of chemical compounds due to difference in their boiling point. The mixture is heated to a temperature at which one or more fractions (component parts) will vaporize. It is a special type of distillation.

Air is a homogeneous mixture of 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases such as helium, krypton, nitrogen dioxide etc.

Consider three gases oxygen, nitrogen and argon whose boiling points are -183, -196, -186 degree celsius, they are to be separated from air using fractional distillation.

Air is compressed by increasing the pressure and then cooled by decreasing the temperature in order to get liquid air. This liquid air is allowed to warm-up slowly in a fractional distillation column, where gases get separated at different heights depending upon their boiling points. As the height of tower increases the temperature increases.

Statement: The temperature is ____ at the base of the fractional distillation column.