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:
1. For polynomial 2x^{2} - 3x^{5} + 5x^{6}.
We observe that the above polynomial has three terms. Here the first term is 2x
^{2}, the second term is -3x
^{5} and the third term is 5x
^{6}.
Now we will determine the exponent of each term.
(i) the exponent of the first term 2x
^{2} = 2
(ii) the exponent of the second term 3x
^{5} = 5
(iii) the exponent of the third term 5x
^{6} = 6
Since, the greatest exponent is 6, the degree of 2x
^{2} - 3x
^{5} + 5x
^{6} is also 6.
Therefore, the degree of the polynomial 2x
^{2} - 3x
^{5} + 5x
^{6} = 6.
2. Find the degree of the polynomial 16 + 8x – 12x^{2} + 15x^{3} - x^{4}.
We observe that the above polynomial has five terms. Here the first term is 16, the second term is 8x, the third term is – 12x
^{2}, the fourth term is 15x
^{3} and the fifth term is - x
^{4}.
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 – 12x
^{2} = 2
(iv) the exponent of the fourth term 15x
^{3} = 3
(v) the exponent of the fifth term - x
^{4} = 4
Since, the greatest exponent is 4, the degree of 16 + 8x – 12x
^{2} + 15x
^{3} - x
^{4} is also 4.
Therefore, the degree of the polynomial 16 + 8x – 12x
^{2} + 15x
^{3} - x
^{4} = 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.
4. Find the degree of a polynomial 11x^{3} - 13x^{5} + 4x.
We observe that the above polynomial has three terms. Here the first term is 11x
^{3}, the second term is - 13x
^{5} and the third term is 4x.
Now we will determine the exponent of each term.
(i) the exponent of the first term 11x
^{3} = 3
(ii) the exponent of the second term - 13x
^{5} = 5
(iii) the exponent of the third term 4x = 1
Since, the greatest exponent is 5, the degree of 11x
^{3} - 13x
^{5} + 4x is also 5.
Therefore, the degree of the polynomial 11x
^{3} - 13x
^{5} + 4x = 5.
5. Find the degree of the polynomial 1 + x + x^{2} + x^{3}.
We observe that the above polynomial has four terms. Here the first term is 1, the second term is x, the third term is x
^{2} and the fourth term is x
^{3}.
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 x
^{2} = 2
(iv) the exponent of the fourth term x
^{3} = 3
Since, the greatest exponent is 3, the degree of 1 + x + x
^{2} + x
^{3} is also 3.
Therefore, the degree of the polynomial 1 + x + x
^{2} + x
^{3} = 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.
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● Terms of an Algebraic Expression
Types of Algebraic Expressions
Degree of a Polynomial
Addition of Polynomials
Subtraction of Polynomials
Power of Literal Quantities
Multiplication of Two Monomials
Multiplication of Polynomial by Monomial
Multiplication of two Binomials
Division of Monomials
Algebra Page
6th Grade Page
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