x³ - 9x + 3x⁵. Determine the degree of the following polynomial
Solution:
Given, the polynomial is x³ - 9x + 3x⁵
We have to find the degree of the polynomial.
The highest degree exponent term of the polynomial is known as the degree of the polynomial.
Types of polynomial based on degree,
1) zero polynomial - all the coefficients of the polynomial are zero.
2) Constant polynomial - polynomial with highest degree as zero, it has no variable only constants.
3) Linear polynomial - polynomial with highest degree as one
4) Quadratic polynomial - polynomial with highest degree as two
5) Cubic polynomial - polynomial with highest degree as three.
6) Bi-Quadratic or quartic polynomial - polynomial with highest degree as four.
7) Quintic polynomial - polynomial with highest degree as five
8) Sextic or hexic polynomial - polynomial with highest degree as 6
9) Septic or heptic polynomial - polynomial with highest degree as 7
In x³ - 9x + 3x⁵, the highest degree exponent of x is five.
x³ - 9x + 3x⁵ is a polynomial with degree 5.
Therefore, the degree of the polynomial is five.
✦ Try This: Determine the degree of the following polynomial : y² + 1
Given, the polynomial is y² + 1
We have to find the degree of the polynomial.
The highest degree exponent of y in y² + 1 is two.
y² + 1 is a quadratic polynomial
Therefore, the degree of the polynomial is two.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 2(iii)
x³ - 9x + 3x⁵. Determine the degree of the following polynomial
Summary:
x³ - 9x + 3x⁵ is a quintic degree polynomial. The degree of the polynomial is five
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