To determine whether the polynomial is in standard form, we need to understand what standard form means for a polynomial. A polynomial is in standard form if the exponents (degrees) of its terms are arranged in descending order, from highest to lowest.
Let's start by identifying and inserting the missing term into the polynomial. The missing term has a degree of 5 and a coefficient of 16, so the term is [tex]\( 16x^5 \)[/tex].
Given polynomial:
[tex]\[
\square + 13x^6 - 11x^3 - 9x^2 + 5x - 2
\][/tex]
Inserting the missing term [tex]\( 16x^5 \)[/tex]:
[tex]\[
13x^6 + 16x^5 - 11x^3 - 9x^2 + 5x - 2
\][/tex]
Now, let's list the terms of the polynomial along with their exponents:
[tex]\[
13x^6, \quad 16x^5, \quad -11x^3, \quad -9x^2, \quad 5x, \quad -2
\][/tex]
Check the exponents to ensure they are in descending order:
[tex]\[
6, 5, 3, 2, 1, 0
\][/tex]
Clearly, the exponents are arranged in descending order. Therefore, the polynomial is in standard form.
The correct statement is:
"It is in standard form because the exponents are in order from highest to lowest."
So, the final answer is:
[tex]\[
\boxed{\text{It is in standard form because the exponents are in order from highest to lowest.}}
\][/tex]
