POLYNOMIALS (LECTURE 2)

LESSON 2 POLYNOMIALS

GOOD MORNING EVERYONE!!

In the previous class we discussed about 
1What is a polynomial?
2. The terms and degree of a polynomial

TODAY'S LEARNING OUTCOMES:
I WILL BE ABLE TO:
1. CLASSIFY THE POLYNOMIALS ON THE BASIS OF NUMBER OF TERMS AND DEGREE.
2. COMPREHEND AND MEMORIZE ABOUT SOME SPECIAL POLYNOMIALS.

                               READ,VIEW AND UNDERSTAND



HOW TO CLASSIFY POLYNOMIALS ON THE BASIS OF NUMBER OF TERMS?

YOU HAVE DONE THIS IN CLASS 8 IN THE CHAPTER 
"ALGEBRAIC EXPRESSIONS"




How many terms are there in each of these? 
1.p(x) = 2x² + 5x – 3 


NO. OF TERMS= 3



2.q(x) = x¹ –1

NO. OF TERMS = 2


3.r(y) = y³  

NO. OF TERMS = 1

4.s(u) = 2 – u – u² + 6u⁵

NO. OF TERMS = 4

In the above examples, p(x) is known as trinomial
                                       q(x) is known as binomial
                                       r(y) is known as monomial
                                       s(u) is known as quadrinomial


                                     

HOW TO CLASSIFY POLYNOMIALS ON THE BASIS OF DEGREE?

You learnt about the DEGREE of a polynomial in the previous class

Today we will do the classification.

watch this☟

.

⭕Now you can identify a linear ,quadratic and a cubic polynomial

look at the IMAGE below and answer the following

1.WRITE THE LINEAR POLYNOMIAL(S).

3x,2x -1

HOW MANY MAXIMUM TERMS ARE THERE IN LINEAR POLYNOMIAL?

2

2WRITE THE QUADRATIC POLYNOMIAL(S)

x² , 2x² + 5 , 3x²  + 5x +1

HOW MANY MAXIMUM TERMS ARE THERE IN QUADRATIC POLYNOMIAL?

3

3WRITE THE CUBIC  POLYNOMIAL(S)

.x³  ,  x³  +  1  ,  x³  +  1 +x  , x³  +  1  +x² +x

.

HOW MANY MAXIMUM TERMS ARE THERE IN CUBIC POLYNOMIAL?

4  

DID YOU OBSERVE?

 IN ABOVE EXAMPLES

THAT MAXIMUM NO. OF TERMS = DEGREE OF THE POLYNOMIAL +1

NOW, YOU WILL LEARN ABOUT 2 SPECIAL POLYNOMIALS

WATCH THIS ☟

                          CLASS WORK  (WRITE DOWN)

I       CLASSIFICATION OF POLYNOMIALS 

A. ON THE BASIS OF NO. OF TERMS

❄❄

A polynomial can have any (finite) number of terms.

B. ON THE BASIS OF DEGREE

MAXIMUM NUMBER OF TERMS IN A POLYNOMIAL  = DEGREE +1

II CONSTANT POLYNOMIAL

EVERY NON ZERO  CONSTANT LIKE 2 , 1/2 OR  0.5 CAN  BE WRITTEN AS  

 2xº ,1/2(xº)  or 0.5(xº)      (❄  as   xº =1)

These are known as CONSTANT polynomials . The degree of non zero  constant polynomial is 0.

III  ZERO POLYNOMIAL

The constant  0 is known as zero polynomial.

Since 0 can be written as  0  xº  / 0 x¹ /0 x² or 0x⁹

so we can say that degree of zero polynomial. is NOT DEFINED

EX 2.1

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

Ans. The binomial of degree 35 can be x³⁵ + 9.

The monomial of degree 100 can be  t¹ºº.

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

Ans. (i)x² +x

We can observe that the degree of the polynomial is 2.

Therefore, we can conclude that the polynomial is a  quadratic polynomial.

(ii) x - x³

We can observe that the degree of the polynomial  is 3.

Therefore, we can conclude that the polynomial is a cubic polynomial.

(iii) y + y ² +4

We can observe that the degree of the polynomial  is 2.

Therefore, the polynomial  is a quadratic polynomial.

                                          

HOME WORK

EX2.1

Q5 (IV) TO (VII)

WE WILL END OUR CLASS HERE!

SEE YOU FOR THE NEXT CLASS!