Question

determine the degree of each monomial.

4 degree:

(2x) degree:

(4r^2s^3) degree:

(3xy^2) degree:

Explanation:

🆕 New Concept Discovered: Degree of a Monomial
Summing exponents of all variables in a term

Step 1: Understand the degree of a monomial

The degree of a monomial is the sum of the exponents of all its variables.

• A non-zero constant (like a plain number) has no variables, which means its variables have an exponent of \(0\). Its degree is \(0\).
• If a variable has no written exponent (like \(x\)), its exponent is understood to be \(1\).
• If there are multiple variables multiplied together, we add their exponents.

Step 2: Find the degree of \(4\)

The number \(4\) is a constant term with no variables. We can think of it as \(4x^0\).

• Exponent: \(0\)
• Degree: \(0\)

Step 3: Find the degree of \(2x\)

The term \(2x\) has a single variable, \(x\), with no written exponent. This is equivalent to \(2x^1\).

• Exponent: \(1\)
• Degree: \(1\)

Step 4: Find the degree of \(4r^2s^3\)

The term \(4r^2s^3\) has two variables: \(r\) and \(s\). We add their exponents together:

• Exponent of \(r\): \(2\)
• Exponent of \(s\): \(3\)
• Sum: \(2 + 3 = 5\)
• Degree: \(5\)

Step 5: Find the degree of \(3xy^2\)

The term \(3xy^2\) has two variables: \(x\) and \(y\). Remember that \(x\) is equivalent to \(x^1\). We add their exponents together:

• Exponent of \(x\): \(1\)
• Exponent of \(y\): \(2\)
• Sum: \(1 + 2 = 3\)
• Degree: \(3\)

Answer:

• 4 $

ightarrow$ Degree: 0

• 2x $

ightarrow$ Degree: 1

• 4r²s³ $

ightarrow$ Degree: 5

• 3xy² $

ightarrow$ Degree: 3