LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

DEGREE OF A POLYNOMIAL

__Degree of a Polynomial__-

**The degree of a polynomial in one variable is the highest index of powers of the
variable in any term of the polynomial.**

**Example.1)
The degree of the polynomial a⁴ + 3a² + 4 in the variable ‘a’ is 4 since this
is the highest index of the powers of ‘a’ in the terms**

**Example.2)
Similarly, the degree of the polynomial 5 x⁸ + 12 x⁵ - 8 x² is 8 since the
highest of the indices of power of x is 8.**

**Example.3)
Similarly, the degree of the polynomial 10 z⁶ - 12 z⁴ + 4 zᶟ is 8 since the highest of the indices
of power of x is 8.**

**The degree of a polynomial in more than one variable is the highest of the sums of the
indices of power of the variables in any of the terms of the polynomial.**

**Example.1)
The expression 8 x⁶y⁴z + 7 xy²z⁵ - 10 x²y⁵z² is a polynomial in x, y & z. The degree of it’s terms are 6, 5, & 5
respectively. So the degree of the polynomial is ( 6 + 1 + 2 ) = 9 **

**Polynomials
are called by particular names in accordance with their degrees,**

**A) A polynomial of degree 1 is to be considered as a linear polynomial. **

**Example.1) x + 8 is a linear polynomial in one variable
‘x’**

**Example.2) - 4x + 8y is a linear polynomial in two variables ( a & b )**

**Example.3) 7a + 8b – 5c is a linear polynomial in three variables (x, y & z)**

**B) A polynomial of degree 2 is ****to be considered as ****a quadratic polynomial.**

**Example.1) 5 a², 16a² + 4 a, 8a² + 5 are quadratic
polynomials in one variable.**

**Example.2) 8 a²b + 7b, 6a²b² + 4 ab, 8a²b² + 5ab² are quadratic polynomials in two variables.**

**Example.3) 8 a²bc + 7ab + 10 a, 6a²b² + 4 abc², and 4a²b²c + 3ab²c
are quadratic polynomials in three
variables.**

**C) A polynomial of degree 3 is ****to be considered as ****a cubic polynomial.**

**Example.1) 5aᶟ
- 3a² + 2, - 3 xᶟ + 2 x, and 5 y² - 2 yᶟ + 8 are cubic polynomials in one variable.**

**Example.2) 8aᶟb²
- 3a²b + 2, - 3 xᶟy - 5 xy², and 3 xy² - 6 xyᶟ + 12 are cubic polynomials in two variables.**

**Examples.3) 3xᶟy + 5 x²yzᶟ - 6 xᶟy, 6x²yᶟ - 7 xz, and
8x²zᶟ - 9xzᶟ are cubic polynomials in three
variables.**

**D) A polynomial of degree 3 is to be considered as a quartic polynomial.**

**Example.1)
3x⁴ - 3aᶟ + 2x, - 8 xᶟ - 6 x⁴, and 12 y⁴ - 2 yᶟ + 8 are quartic polynomials in one variable.**

**Example.2) 10aᶟb⁴
- 3a²b + 8, - 6 xᶟy⁴ + 8 xᶟy², and 3 xy²- 7 x⁴y + 12 are quartic polynomials in two
variables.**

**Examples.3) 3xᶟyz⁴ + 5 yzᶟ - 8 xᶟy, 6x²yᶟ - 3 xy⁴z, and
8x²yz⁴ - 9xz are quartic polynomials in three
variables.**

**Examples.4) 8wxᶟyz⁴ + 6 xyzᶟ - 8 xᶟw, 6 wx⁴yᶟ - 3 xy⁴z,
and 8 wx²yz⁴ - 9x²z are quartic polynomials in four
variables.**