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