Degree of the Polynomial

Degree of the Polynomial is the exponent of the highest degree term in a polynomial.

A polynomial of degree 0 is called a Constant Polynomial.

On the basis of Degree of the Polynomial,there are different types of polynomial. They are as follows :

Degree	Name of the Polynomial	Form of the Polynomial	Example
0	Constant Polynomial	f(x) = a, a is a constant.	f(x) = 2
1	Linear Polynomial	f(x) = ax + b , a ≠ 0	f(x) = 3x + 4
2	Quadratic Polynomial	f(x) = ax2 + bx + c , a ≠ 0	f(x) = 2x2 + 4x - 4
3	Cubic Polynomial	f(x) = ax3 + bx2 + cx + d , a ≠ 0	f(x) = 3x3 - x2 + 4x + 5
4	Quartic Polynomial	f(x) = ax4 + bx3 + cx2 + dx + e , a ≠ 0	f(x) = - 4x4 + 3x3 - x2 + 8x + 6

Write the degree of the following polynomial

1) f(x) = 3x + 1/2

Solution :
The degree of this polynomial is 1 as the highest exponent is 1.

2) p(x) = 2y ² - 3y/2 + 7.

Solution :
The highest exponent is 2, so its degree is 2.

3) q(x) = 5x ³ - 3x ² + x - 1/√2.

Solution :
The degree of this polynomial is 3 as it is the highest exponent.

4) q(u) = 9u ⁵ - 2/3 u ⁴ + u ² -1/2.

Solution :
The degree of this polynomial is 5.

5) p(x) = -3/2

Solution :
The degree of this polynomial is 0, so it is a Constant Polynomial .

6) q(x) = 1

Solution :
The degree of this polynomial is 0, so it is a Constant Polynomial .

Identify the types of polynomial

1) p(x) = x ² -5x + 6

Solution :
The degree of this polynomial is 1 so its a Linear polynomial.

2) q(y) = y ³ - 2y ² + 8

Solution :
Degree = 3
∴ Polynomial = Cubic polynomial.

3) f(x) = 4x ⁴ + 9

Solution :
Degree = 4
∴ Polynomial = Quartic.

4) q(a) = a ⁵ + 4a ³ -10

Solution :
Degree = 5
∴ Polynomial = Polynomial ( no special name as such).

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Polynomial

• Degree of the Polynomial
• Zeros of Polynomial
• Remainder Theorem
• Find remainder by Synthetic Division
• Rational root test in Polynomial
• Solved Examples on Polynomial

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