POLYNOMIALS LESSON 1
In this chapter we will learn about a particular type of algebraic expression, called polynomial.
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.
(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 !!
