Identify the binomial
A) [tex]$x^2-4$[/tex]
B) [tex]$x^2$[/tex]
C) [tex]$2 x^2+3 x-1+y$[/tex]
D) [tex]$x^2-4 x+2$[/tex]
Answer (1)
The problem requires identifying a binomial from a list of polynomials. A binomial is a polynomial with two terms. By examining each option, we find that x 2 − 4 is the only expression with exactly two terms. Therefore, the binomial 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 the Options Let's examine each option: A) x 2 − 4 has two terms: x 2 and − 4 .
B) x 2 has one term: x 2 .
C) 2 x 2 + 3 x − 1 + y has four terms: 2 x 2 , 3 x , − 1 , and y .
D) x 2 − 4 x + 2 has three terms: x 2 , − 4 x , and 2 .
Identifying the Binomial The expression with exactly two terms is the binomial. Therefore, the binomial is x 2 − 4 .
Examples
Binomials are commonly used in algebra and calculus. For example, when expanding ( x + a ) 2 , we get x 2 + 2 a x + a 2 , which involves binomial coefficients. Understanding binomials is crucial for simplifying algebraic expressions and solving equations. In real life, binomials can model situations with two possible outcomes, such as success or failure in probability problems.
