What Is The Degree Of A Polynomial?
Degree of a polynomial
Polynomials are the main part of algebra and the understanding the polynomials makes algebra easy. In this presentation I am going to explain the degree of a polynomial. Many of my students wonder, when I introduce them with the degree of the polynomials because they are learning about the degree of an angle since grade four or five but degree of a polynomial is new to them. Students are also aware about degree of temperature since their elementary grades, but not about degree of a polynomial till grade 8 or 9.
So, what is the degree of a polynomial?
Degree of a polynomial is the highest power of a term in a polynomial. Therefore, this degree is not like the degree of an angle or degree centigrade temperature, but the degree of a polynomial is all about the exponents or powers of variables in the polynomials.
To understand the concept mathematically, consider the following examples of polynomials having different degrees:
1. 2
2. 2a
3. 3a²
4. 3a²+ 5
5. 2a²b³c
6. 2a²+ 3abc – 9
7. x³ + 2x² – 3x + 2
8. x³y + x²y³z – 6
Solutions:
1. In problem number one, “2” is constant polynomial that is a polynomial without any variable. The degree of constant polynomials is “zero”. So the degree of the monomial “2” is zero.
2. In problem number two, “2a” is a monomial with variable “a” having power one, hence the degree of monomial “2a” is l (power of the variable).
3. In problem number three, “3a²” is again a monomial with the variable “a” having power “2”, hence the degree of monomial “3a²” is 2(power of the variable).
4. In problem number four, “3a²+ 5” is a binomial with the variable “a” having power two, hence the degree is 2.
5. In problem number five, “2a²b³c” is a monomial with three variables, “a”, “b” and “c”. In a polynomial when a term has more than one variable, add the powers of all the variables to find the degree of that term.
So, add the powers of variables “a”, “b” and “c”. As “a” got power “2”, “b” got power “3” and “c” got power “1”.
By adding 3, 2 and 1, we get 6 which is the degree of the monomial “2a²b³c”.
6. In problem number six, “2a²+ 3abc – 9” is a trinomial involving three variables. In first term there is only one variable “a” with degree two, the second term have three variables with degree one each, but to find the degree of the second term add all the powers of the variables. So, by adding powers of “a”, “b” and “c” in term two we get its degree equal to 3. Third term is “- 9”, a constant, hence with degree zero. Now the degree of this trinomial is represented by its second term as it has the highest power which is “3”, hence the degree of the given trinomial is “3”.
7. In problem number seven, “x³ + 2x² – 3x + 2” is polynomial with four terms and highest power is “3” hence the degree is “3”.
8. In problem number eight, “x³y + x²y³z – 6” is again a trinomial with many variables. But the second term has the highest power (add all the powers of the variables) which is equal to “6”. Hence the degree of the trinomial is given by its second term and is “6”.
