Pick the expression that matches this description:
A monomial of the [tex]$2^{\text {rd }}$[/tex] degree with a leading coefficient of 3
A. [tex]$3 n^2$[/tex]
B. [tex]$3 n-n^2$[/tex]
C. [tex]$3 n^2-1$[/tex]
D. [tex]$2 n^3$[/tex]
Answer (1)
A monomial is a single-term expression.
The degree of a monomial is the exponent of the variable.
The leading coefficient is the number multiplying the variable.
The expression that is a monomial of the second degree with a leading coefficient of 3 is 3 n 2 .
Explanation
Understanding the Requirements We need to identify the expression that is a monomial of the second degree with a leading coefficient of 3. Let's break down what each of these terms means.
Key Definitions A monomial is a single term expression. The degree of a monomial is the exponent of the variable. The leading coefficient is the number that multiplies the variable.
Analyzing Each Option Now, let's examine each option:
(A) 3 n 2 : This is a single term (monomial). The exponent of n is 2, so it's of the second degree. The coefficient is 3. This matches the description. (B) 3 n − n 2 : This has two terms, so it's not a monomial. (C) 3 n 2 − 1 : This has two terms, so it's not a monomial. (D) 2 n 3 : This is a single term (monomial). The exponent of n is 3, so it's of the third degree, not the second. The coefficient is 2, not 3.
Conclusion Therefore, the expression that matches the description is 3 n 2 .
Examples
Monomials are fundamental building blocks in algebra. For instance, when calculating the area of a square with side length 's', the area is s^2, which is a monomial of degree 2. Similarly, if you are calculating the volume of a cube with side length '2x', the volume is (2x)^3 = 8x^3, which is a monomial of degree 3. Understanding monomials helps in simplifying and solving various algebraic problems.
