Identifying the Polynomial- Deciphering the Correct Option from the Given Choices

Which of the following is polynomial? This question often arises in the realm of mathematics, particularly when dealing with polynomial functions. Polynomials are a fundamental concept in algebra and play a crucial role in various mathematical fields. In this article, we will explore the definition of a polynomial, its properties, and examples to help you identify which of the given options is a polynomial.

A polynomial is an expression consisting of variables and coefficients, combined using the operations of addition, subtraction, multiplication, and non-negative integer exponents. The general form of a polynomial is:

f(x) = a_n x^n + a_{n-1} x^{n-1} + … + a_1 x + a_0

where ‘a_n’, ‘a_{n-1}’, …, ‘a_1’, and ‘a_0’ are constants, and ‘n’ is a non-negative integer representing the degree of the polynomial. The term ‘a_n’ is called the leading coefficient, and ‘x^n’ is the leading term.

Now, let’s consider some examples to better understand polynomials:

1. 2x^3 – 5x^2 + 3x – 1: This is a polynomial of degree 3, as the highest power of the variable ‘x’ is 3.

2. 4x^2 + 7: This is a polynomial of degree 2, as the highest power of ‘x’ is 2.

3. 5x^4 – 3x^3 + 2x^2 – x + 1: This is a polynomial of degree 4, as the highest power of ‘x’ is 4.

4. 8x^5 – 6x^3 + 4x^2 – 2x + 1: This is a polynomial of degree 5, as the highest power of ‘x’ is 5.

Now, let’s address the main question: which of the following is a polynomial? Given the options, you can determine the correct answer by identifying the expression that follows the general form of a polynomial. Remember to check for the presence of variables, coefficients, and non-negative integer exponents.

For instance, if the options are:

A) 2x^3 – 5x^2 + 3x – 1
B) 7x^4 – 2x^3 + 3x^2 – 4x + 1
C) 5x^2 + 6
D) 4x^5 – 3x^4 + 2x^3 – x^2 + 1

The correct answer would be:

A) 2x^3 – 5x^2 + 3x – 1

This expression follows the general form of a polynomial and has a degree of 3. By understanding the definition and properties of polynomials, you can now confidently identify which of the given options is a polynomial.