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) = ax^{2} + bx + c , a ≠ 0 | f(x) = 2x^{2} + 4x - 4 |
3 | Cubic Polynomial | f(x) = ax^{3} + bx^{2} + cx + d , a ≠ 0 | f(x) = 3x^{3} - x^{2} + 4x + 5 |
4 | Quartic Polynomial | f(x) = ax^{4} + bx^{3} + cx^{2} + dx + e , a ≠ 0 | f(x) = - 4x^{4} + 3x^{3} - x^{2} + 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