Question

what is the degree of (4x^5y^2 + 2xy^3)?

• 5
• 7
• 10
• 11

Explanation:

🆕 New Concept Discovered: Degree of a Polynomial
The highest sum of exponents in any single term.

Step 1: Identify the terms of the polynomial

The given polynomial is:

$$ -4x^5 y^2 + 2x y^3 $$

This expression consists of two terms:

1. First term: \( -4x^5 y^2 \)
2. Second term: \( 2x y^3 \) (where \( x \) is implicitly \( x^1 \))

Step 2: Find the degree of each term

To find the degree of a term with multiple variables, add the exponents of all the variables in that term:

• For \( -4x^5 y^2 \):

$$ \text{Degree} = 5 + 2 = 7 $$

• For \( 2x^1 y^3 \):

$$ \text{Degree} = 1 + 3 = 4 $$

Step 3: Determine the degree of the polynomial

The degree of a polynomial is the highest degree among all of its individual terms.

Comparing the degrees of the terms:

$$ \max(7, 4) = 7 $$

The degree of the polynomial is \( 7 \).

Answer:

7