y³(1 - y⁴). Determine the degree of the following polynomial
Solution:
Given, the polynomial is y³(1 - y⁴)
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
By multiplicative and distributive property,
y³(1 - y⁴) = y³ - y⁷
In y³ - y⁷, the highest degree exponent of y is seven.
y³ - y⁷⁵ is a septic polynomial
Therefore, the degree of the polynomial is seven
✦ Try This: Determine the degree of the following polynomial : y³ + 1
Given, the polynomial is y³ + 1
We have to find the degree of the polynomial.
The highest degree exponent of y in y³ + 1 is two.
y³ + 1 is a cubic polynomial
Therefore, the degree of the polynomial is three.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 2(iv)
y³(1 - y⁴). Determine the degree of the following polynomial
Summary:
A polynomial is a type of expression in which the exponents of all variables should be a whole number. y³(1 - y⁴) is a septic degree polynomial. The degree of the polynomial is seven
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