Which of these expressions is a binomial?
| Expression |
| :---------- | :------- |
| 1 | -8 |
| 2 | [tex]$7 a$[/tex] |
| 3 | [tex]$3+4 x$[/tex] |
A. 2 and 3
B. 1 and 2
C. 1
D. 3
Answer (2)
A binomial is an expression with two terms.
Expression 1 (-8) has one term.
Expression 2 ( 7 a ) has one term.
Expression 3 ( 3 + 4 x ) has two terms, so it is a binomial. The answer is 3 .
Explanation
Understanding Binomials A binomial is an algebraic expression that has two terms. We need to identify which of the given expressions fits this definition.
Analyzing Expression 1 Expression 1: -8. This expression has only one term, which is a constant. Therefore, it is not a binomial.
Analyzing Expression 2 Expression 2: 7 a . This expression has only one term, which is a variable term. Therefore, it is not a binomial.
Analyzing Expression 3 Expression 3: 3 + 4 x . This expression has two terms: a constant term (3) and a variable term ( 4 x ). Therefore, it is a binomial.
Conclusion Based on our analysis, only expression 3 is a binomial. Therefore, the correct answer is 3.
Examples
Binomials are useful in many real-world situations. For example, when calculating the area of a rectangle with sides (x + 2) and (x + 3), you use binomial multiplication. The area is represented by the expression ( x + 2 ) ( x + 3 ) , which expands to x 2 + 5 x + 6 . Understanding binomials helps in simplifying such expressions and solving related problems in geometry and algebra.
Only expression 3, which is 3 + 4x, is a binomial because it consists of two distinct terms. Expressions 1 and 2 contain only one term each, so they do not qualify as binomials. Therefore, the answer is D. 3.
;
