Question

which term describes the polynomial (6 + 3x + 4y)?

cubic trinomial
constant binomial
quadratic binomial
linear trinomial

Explanation:

🆕 New Concept Discovered: Classifying Polynomials
Naming polynomials by degree and number of terms.

Step 1: Count the number of terms

A polynomial is classified by the number of terms it has, which are separated by addition or subtraction signs:

• Monomial: 1 term
• Binomial: 2 terms
• Trinomial: 3 terms

The given expression is:

$$ 6 + 3x + 4y $$

There are 3 distinct terms: \(6\), \(3x\), and \(4y\). Therefore, it is a trinomial.

Step 2: Determine the degree of the polynomial

The degree of a polynomial is the highest exponent of its variables in any single term:

• Constant (degree 0): No variables (e.g., \(6\))
• Linear (degree 1): Highest exponent is 1 (e.g., \(x^1\) or \(y^1\))
• Quadratic (degree 2): Highest exponent is 2 (e.g., \(x^2\))
• Cubic (degree 3): Highest exponent is 3 (e.g., \(x^3\))

In our polynomial \(6 + 3x + 4y\):

• The term \(6\) has degree 0.
• The term \(3x\) (which is \(3x^1\)) has degree 1.
• The term \(4y\) (which is \(4y^1\)) has degree 1.

The highest degree of any term is 1, which makes it linear.

Step 3: Combine the classifications

Combining the degree classification and the number of terms classification:

• Degree 1 \(

ightarrow\) linear

• 3 terms \(

ightarrow\) trinomial

Thus, the polynomial is a linear trinomial.

Answer:

linear trinomial