Introduction to Linear Polynomials | Exercise 2.1
Question 2
Write polynomials of degrees 1, 2 and 3.
Solution
Understand the Question
- The degree of a polynomial is the highest exponent (power) of the variable in the expression.
- Degree 1 (Linear polynomial): The highest power of the variable is .
- Degree 2 (Quadratic polynomial): The highest power of the variable is .
- Degree 3 (Cubic polynomial): The highest power of the variable is .
Step 1 · Polynomial of Degree 1
A polynomial of degree is called a linear polynomial, where the highest power of the variable is .
An example is:
Step 2 · Polynomial of Degree 2
A polynomial of degree is called a quadratic polynomial, where the highest power of the variable is .
An example is:
Step 3 · Polynomial of Degree 3
A polynomial of degree is called a cubic polynomial, where the highest power of the variable is .
An example is:
Answer
- Degree 1:
- Degree 2:
- Degree 3:
Common Mistakes
- Degree vs. Number of Terms: Confusing the degree (highest exponent) with the number of terms. For example, has only term but is of degree .
- Zero Leading Coefficient: Writing a polynomial where the highest degree term has a coefficient of zero (e.g., is a degree polynomial, not degree ).