Question

which polynomials are in standard form? choose all answers that apply: a 10 - n b 5n + 3n³ - 1 c n + 4n² - 7n³ d none of the above

Explanation:

To determine if a polynomial is in standard form, we check if the terms are ordered from the highest degree to the lowest degree.

Step 1: Analyze Option A

The polynomial \(10 - n\) can be rewritten as \(-n + 10\). The term with the highest degree (degree 1 for \(-n\)) comes first, followed by the constant term (degree 0 for \(10\)). So, this is in standard form.

Step 2: Analyze Option B

The polynomial \(5n + 3n^3 - 1\) has terms with degrees 1, 3, and 0. The highest degree term is \(3n^3\) (degree 3), but it is not the first term. The first term is \(5n\) (degree 1), so this is not in standard form. It should be \(3n^3 + 5n - 1\) to be in standard form.

Step 3: Analyze Option C

The polynomial \(n + 4n^2 - 7n^3\) has terms with degrees 1, 2, and 3. The highest degree term is \(-7n^3\) (degree 3), but it is not the first term. The first term is \(n\) (degree 1), so this is not in standard form. It should be \(-7n^3 + 4n^2 + n\) to be in standard form.

Answer:

A. \(10 - n\)