POLYNOMIALS ( LECTURE 1)

POLYNOMIALS LESSON 1

You have studied algebraic expressions, their addition, subtraction, multiplication and division in earlier classes

In this chapter we will learn about  a particular type of algebraic expression, called polynomial.

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TODAY'S LEARNING OUTCOMES

I WILL BE ABLE TO

1. RECALL WHAT IS AN ALGEBRAIC EXPRESSION AND DEFINE POLYNOMIAL.

2. RECALL AND DEFINE TERMS AND COEFFICIENTS.

3. DEFINE DEGREE OF A POLYNOMIAL

READ,VIEW AND UNDERSTAND

LOOK AT THE IMAGE BELOW

WRITE DOWN THE POWER OF VARIABLE IN EACH TERM.

A.  First term 2/x²  = 2x-² (remember 1/x² = x-²)

      second  term  = x  =xˡ

B First term  x² 

    second  term √2x =√2xˡ

C First term    x² 

    second  term  2√x =2 xˡ/² (remember √  means 1/2 as exponent)

 D First term  x-²

   second  term  xˡ

 E  First term    2/3 x²

    second  term xˡ

Now, select the algebraic expressions  having  only whole numbers as the exponents of the variable in each term?

You, can clearly see the answer is B and E

These are  known as POLYNOMIALS

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WHAT ARE TERMS AND COEFFICIENTS OF A POLYNOMIAL?

EG 1. In the polynomial x² + 2x, the expressions x² and 2x are called the terms of the polynomial. 

 COEFFICIENT OF  x² =……1..

COEFFICIENT OF  2x =…….2..….....

2. 3y² + 5y + 7 has three terms, namely, 3y², 5y and 7.

3. Can you write the terms of the polynomial –x³ + 4x² + 7x – 2 ? 

  This polynomial has 4 terms, namely, –x³, 4x², 7x and –2.

COEFFICIENT OF  –x³ =….-1

   

WHAT IS DEGREE OF A POLYNOMIAL?

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NOTE: IN THIS CHAPTER WE WILL LEARN MAINLY ABOUT POLYNOMIALS IN 1 VARIABLE.

                     

EG. Find the degree of each of the polynomials given below: 

(i) x⁵ – x⁴ + 3

The highest power of the variable is 5.

So,the degree is 5

 (ii) 2 – y² – y³ + 2y⁸

the degree of the polynomial is 8.

(iii) 2

The only term here is 2 which can be written as 2x⁰. So the exponent of x is 0. Therefore, the degree of the polynomial is 0.

 

                                                        CLASS WORK 

POLYNOMIAL

 All the algebraic expressions which  have  have only whole numbers as the exponents of the variable.  are called polynomials . 

for  example , x³ – x² + 4x + 7 is a polynomial in x. 

Similarly, 3y² + 5y is a polynomial in variable y.

HOW TO DENOTE A POLYNOMIAL?

 We may denote the polynomial in variable x  by p(x), or q(x), or r(x), etc. 

 for example, we may write : p(x) = 2x² + 5x – 3 

TERMS OF A POLYNOMIAL

The terms of polynomials are the parts  which are generally separated by “+” or “-” signs. 

 For example, in a polynomial, say, 2x2 + 5x +4, the number of terms will be 3

DEGREE OF A POLYNOMIAL

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

So, the degree of the polynomial 3x⁷ – 4x⁶+ x + 9 is 7  

                                          EX2.1

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

(I)4x2 – 3x + 7

We can observe that in the polynomial, we have x as the only variable and the powers of x in each term are a whole number.

Therefore, we conclude that it is a polynomial in one variable.

(ii)  y2 +√ 2

We can observe that in the polynomial, we have y as the only variable and the powers of y in each term are a whole number.

Therefore, we conclude that it is a polynomial in one variable.

(iii)3 √t +t √2

We can observe that in the polynomial, we have t as the only variable and the powers of t in each term are not a whole number.( √t = tˡ/²    and 1/2 is not a whole no.)

Therefore, we conclude that it is not a polynomial in one variable.

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

(i) 2 + x² + x

The coefficient of  x ²in the polynomial  is 1.

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

(i)5x³ + 4x² +7x

We can observe that in the polynomial, the highest power of the variable x is 3.

Therefore, we conclude that the degree of the polynomial  is 3.

(ii)  4 - y²

We can observe that in the polynomial, the highest power of the variable y is 2.

Therefore, we conclude that the degree of the polynomial  is 2.

(iii)5t -√7

We observe that in the polynomial, the highest power of the variable t is 1.

Therefore, we conclude that the degree of the polynomial  is 1.

                                                                           EX2.1

Q1(IV)(V)

Q2 (II)  TO (IV)

Q4(IV)

WE END OUR CLASS HERE!!

COMPLETE YOUR HW AND REVISE CW

SEE YOU TOMORROW  !!