Select the best answer for the question. Identify the binomial.
A. [tex]$2 x^2+3 x-1+y$[/tex]
B. [tex]$x^2-4$[/tex]
C. [tex]$x^2-4 x+2$[/tex]
D. [tex]$x^2$[/tex]

A binomial is a polynomial with exactly two terms. From the options provided, the correct binomial is x 2 − 4 , found in Option B. This option meets the criteria, having exactly two terms compared to the others, which contain one, three, or four terms.
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Answered by Anonymous | 2025-07-07

A binomial is a polynomial with two terms.
Option A has four terms, Option B has two terms, Option C has three terms, and Option D has one term.
The binomial is the option with two terms.
Therefore, the answer is x 2 − 4 ​ .

Explanation

Understanding Binomials A binomial is a polynomial with exactly two terms. We need to identify which of the given options is a binomial.

Analyzing Each Option Let's examine each option:


Option A: 2 x 2 + 3 x − 1 + y has four terms: 2 x 2 , 3 x , − 1 , and y .
Option B: x 2 − 4 has two terms: x 2 and − 4 .
Option C: x 2 − 4 x + 2 has three terms: x 2 , − 4 x , and 2 .
Option D: x 2 has one term: x 2 .

Identifying the Binomial Based on the definition of a binomial, the option with exactly two terms is the correct answer. Option B, x 2 − 4 , has two terms.

Conclusion Therefore, the binomial is x 2 − 4 .


Examples
Binomials are used in various mathematical and real-world applications. For instance, when calculating the area of a square with side length ( x + a ) , the area is ( x + a ) 2 = x 2 + 2 a x + a 2 . The expression ( x + a ) is a binomial. Understanding binomials helps in simplifying algebraic expressions and solving problems related to areas, volumes, and other mathematical concepts. They also form the basis for more complex polynomial expressions and are crucial in fields like physics and engineering for modeling various phenomena.

Answered by GinnyAnswer | 2025-07-07