Question

find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these.
4x + 0.4
classify the given polynomial.
○ binomial
○ monomial
○ trinomial
○ none of these

Explanation:

Part 1: Find the degree of the polynomial \( 4x + 0.4 \)

Step 1: Recall the definition of the degree of a polynomial

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial.

Step 2: Identify the exponents of the variable in each term

• For the term \( 4x \), the variable \( x \) has an exponent of \( 1 \) (since \( x = x^1 \)).
• For the term \( 0.4 \), we can write it as \( 0.4x^0 \) (because any non - zero number to the power of \( 0 \) is \( 1 \)), so the exponent of \( x \) here is \( 0 \).

Step 3: Determine the highest exponent

Comparing the exponents \( 1 \) and \( 0 \), the highest exponent is \( 1 \). So the degree of the polynomial \( 4x + 0.4 \) is \( 1 \).

Part 2: Classify the polynomial \( 4x + 0.4 \)

Step 1: Recall the definitions of monomial, binomial, and trinomial

• A monomial is a polynomial with exactly one term.
• A binomial is a polynomial with exactly two terms.
• A trinomial is a polynomial with exactly three terms.

Step 2: Count the number of terms in \( 4x + 0.4 \)

The polynomial \( 4x + 0.4 \) has two terms: \( 4x \) and \( 0.4 \). Since it has two terms, it is a binomial.

Answer:

s:

• Degree of the polynomial: \( 1 \)
• Classification of the polynomial: binomial (the option is "binomial")