1 + x + x². Classify the following as a constant, linear, quadratic and cubic polynomials
Solution:
Given, the polynomial is 1 + x + x²
We have to classify the polynomial based on the degree.
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.
The highest degree of exponent in 1 + x + x² is 2.
Therefore, 1 + x + x² is a quadratic polynomial.
✦ Try This: Classify the following as a constant, linear, quadratic and cubic polynomials : 4
Given, the polynomial is 4
We have to classify the polynomial based on the degree.
The highest degree of exponent in 4 is 0
Therefore, 4 is a constant polynomial.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 5(viii)
1 + x + x². Classify the following as a constant, linear, quadratic and cubic polynomials
Summary:
The given polynomial 1 + x + x² is a quadratic polynomial as the highest power of the exponent is 2
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