Question

what term describes the monomial \\(14xyz\\)?

• constant
• linear
• quadratic
• cubic

Explanation:

🆕 New Concept Discovered: Degree of a Monomial
Finding the total power of a term.

Step 1: Identify the exponents of the variables

To classify the monomial \( 14xyz \), we need to find its degree. The degree of a monomial is the sum of the exponents of all its variables.

The variables in the monomial are \( x \), \( y \), and \( z \). Any variable written without an explicit exponent has an implied exponent of \( 1 \):

• The exponent of \( x \) is \( 1 \)
• The exponent of \( y \) is \( 1 \)
• The exponent of \( z \) is \( 1 \)

Step 2: Calculate the degree

Add the exponents of all the variables together:

$$ 1 + 1 + 1 = 3 $$

The degree of the monomial is \( 3 \).

Step 3: Match the degree to the classification term

We classify polynomials and monomials by their degree using specific names:

• Degree \( 0 \): constant
• Degree \( 1 \): linear
• Degree \( 2 \): quadratic
• Degree \( 3 \): cubic

Since the degree of \( 14xyz \) is \( 3 \), the term that describes it is cubic.

Answer:

cubic