Degree of a Polynomial
Here we will learn the basic concept of polynomial and the degree of a polynomial.
What is polynomial?
An algebraic expression which consists of one, two or more terms is called a polynomial.
How to find a degree of a polynomial?
The degree of the polynomial is the greatest of the exponents (powers) of its various terms.
Examples of polynomials and its degree:
We observe that the above polynomial has three terms. Here the first term is 2x2, the second term is -3x5 and the third term is 5x6.
Now we will determine the exponent of each term.
(i) the exponent of the first term 2x2 = 2
(ii) the exponent of the second term 3x5 = 5
(iii) the exponent of the third term 5x6 = 6
Since, the greatest exponent is 6, the degree of 2x2 - 3x5 + 5x6 is also 6.
Therefore, the degree of the polynomial 2x2 - 3x5 + 5x6 = 6.
2. Find the degree of the polynomial 16 + 8x – 12x2 + 15x3 - x4.
We observe that the above polynomial has five terms. Here the first term is 16, the second term is 8x, the third term is – 12x2, the fourth term is 15x3 and the fifth term is - x4.
Now we will determine the exponent of each term.
(i) the exponent of the first term 16 = 0
(ii) the exponent of the second term 8x = 1
(iii) the exponent of the third term – 12x2 = 2
(iv) the exponent of the fourth term 15x3 = 3
(v) the exponent of the fifth term - x4 = 4
Since, the greatest exponent is 4, the degree of 16 + 8x – 12x2 + 15x3 - x4 is also 4.
Therefore, the degree of the polynomial 16 + 8x – 12x2 + 15x3 - x4 = 4.
3. Find the degree of a polynomial 7x – 4
We observe that the above polynomial has two terms. Here the first term is 7x and the second term is -4
Now we will determine the exponent of each term.
(i) the exponent of the first term 7x = 1
(ii) the exponent of the second term -4 = 1
Since, the greatest exponent is 1, the degree of 7x – 4 is also 1.
Therefore, the degree of the polynomial 7x – 4 = 1.
We observe that the above polynomial has three terms. Here the first term is 11x3, the second term is - 13x5 and the third term is 4x.
Now we will determine the exponent of each term.
(i) the exponent of the first term 11x3 = 3
(ii) the exponent of the second term - 13x5 = 5
(iii) the exponent of the third term 4x = 1
Since, the greatest exponent is 5, the degree of 11x3 - 13x5 + 4x is also 5.
Therefore, the degree of the polynomial 11x3 - 13x5 + 4x = 5.
5. Find the degree of the polynomial 1 + x + x2 + x3.
We observe that the above polynomial has four terms. Here the first term is 1, the second term is x, the third term is x2 and the fourth term is x3.
Now we will determine the exponent of each term.
(i) the exponent of the first term 1 = 0
(ii) the exponent of the second term x = 1
(iii) the exponent of the third term x2 = 2
(iv) the exponent of the fourth term x3 = 3
Since, the greatest exponent is 3, the degree of 1 + x + x2 + x3 is also 3.
Therefore, the degree of the polynomial 1 + x + x2 + x3 = 3.
6. Find the degree of a polynomial -2x.
We observe that the above polynomial has one term. Here the term is -2x.
Now we will determine the exponent of the term.
(i) the exponent of the first term -2x = 1
Therefore, the degree of the polynomial -2x = 1.
● Terms of an Algebraic Expression
Types of Algebraic Expressions
Multiplication of Two Monomials
Multiplication of Polynomial by Monomial
Multiplication of two Binomials
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