Question

which statement best describes the polynomial?

(13y^{8} - 4y^{7} + 3y)

• it is in standard form because the coefficients are in order from highest to lowest.
• it is in standard form because the exponents are in order from highest to lowest.
• it is in standard form because there is no constant.
• it is in standard form because the coefficients cannot be further simplified.

Explanation:

🆕 New Concept Discovered: Polynomial Standard Form
Writing terms from highest to lowest exponent

Step 1: Identify the terms and their exponents

The given polynomial is:

$$ 13y^8 - 4y^7 + 3y $$

Let's look at the exponent (degree) of each term from left to right:

• The first term is \( 13y^8 \), which has an exponent of \( 8 \).
• The second term is \( -4y^7 \), which has an exponent of \( 7 \).
• The third term is \( 3y \) (which is \( 3y^1 \)), which has an exponent of \( 1 \).

Step 2: Analyze the order of the exponents

Comparing the exponents from left to right:

$$ 8 > 7 > 1 $$

The exponents are arranged in descending order (from highest to lowest).

Step 3: Match with the definition of standard form

A polynomial is written in standard form when its terms are placed in descending order by their degree (exponents), starting with the largest exponent and ending with the smallest.

Therefore, the correct statement is:
"It is in standard form because the exponents are in order from highest to lowest."

Answer:

It is in standard form because the exponents are in order from highest to lowest.