What is a Polynomial of Degree Zero?

S3-SA1-0346

Grade Level:

Class 7

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A polynomial of degree zero is simply a non-zero constant number. It's a special type of polynomial where the highest power of the variable (like 'x') is zero, meaning the variable itself is not present.

Simple Example

Quick Example

Imagine the price of a small chai at your local tapri is always Rs. 10, no matter how many cups you buy. We can write this as P = 10. Here, '10' is a constant number, and it represents a polynomial of degree zero because there's no variable 'x' with any power changing its value.

Worked Example

Step-by-Step

PROBLEM: Identify the degree of the polynomial: 7

Step 1: Understand what a polynomial is. A polynomial is an expression consisting of variables and coefficients, involving only operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Step 2: Look at the given expression: 7. This is a constant number.
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Step 3: Recall that any constant number 'c' can be written as c * x^0, because any number (except 0) raised to the power of 0 is 1 (x^0 = 1).
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Step 4: So, 7 can be written as 7 * x^0.
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Step 5: The degree of a polynomial is the highest power of the variable in the polynomial. In 7 * x^0, the only power of the variable 'x' is 0.
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Answer: The degree of the polynomial 7 is 0.

Why It Matters

Understanding constant polynomials is crucial in fields like Data Science and Economics, where fixed values or baseline costs are often represented. Engineers use them to model unchanging parameters in systems. They are the building blocks for more complex equations, making them fundamental for many future career paths.

Common Mistakes

MISTAKE: Thinking 0 is a polynomial of degree zero. | CORRECTION: The number 0 is a special case called the 'zero polynomial', and its degree is undefined or sometimes taken as -infinity, not zero.

MISTAKE: Confusing a constant (like 5) with a variable (like 5x). | CORRECTION: A constant '5' has degree zero because x^0 = 1. '5x' has degree one because the power of x is 1.

MISTAKE: Believing that only polynomials with 'x' written out can have a degree. | CORRECTION: Any constant number is a polynomial, and its degree is implicitly zero because it can be written as (constant) * x^0.

Practice Questions

Try It Yourself

QUESTION: What is the degree of the polynomial -15? | ANSWER: 0

QUESTION: Is the expression '2/3' a polynomial of degree zero? Explain why. | ANSWER: Yes, because 2/3 is a constant number and can be written as (2/3) * x^0.

QUESTION: If the number of laddoo in a box is always 12, write this as a polynomial and state its degree. | ANSWER: P = 12 (or 12x^0). The degree is 0.

MCQ

Quick Quiz

Which of the following is a polynomial of degree zero?

x + 5

100

x^2

The Correct Answer Is:

A polynomial of degree zero is a non-zero constant. Option B (100) is a non-zero constant. Options A and C have variables with powers greater than zero. Option D (0) is the zero polynomial, which has an undefined degree.

Real World Connection

In the Real World

Think about online shopping in India. When you buy something for a fixed price, say a T-shirt for Rs. 499, that price is a constant. In the background, the e-commerce website's system might represent this fixed price as a polynomial of degree zero, like 'Price = 499', which remains constant regardless of other factors.

Key Vocabulary

Key Terms

POLYNOMIAL: An expression with variables, coefficients, and non-negative integer exponents | DEGREE: The highest power of the variable in a polynomial | CONSTANT: A number whose value does not change | COEFFICIENT: A numerical factor multiplied with a variable

What's Next

What to Learn Next

Great job understanding constant polynomials! Next, you should explore 'Polynomials of Degree One'. This will help you understand how variables change values and how equations represent real-world situations like calculating auto-rickshaw fares based on distance.