Answered

The missing term in the following polynomial has a degree of 5 and a coefficient of 16:
[tex]16x^5 + 13x^6 - 11x^3 - 9x^2 + 5x - 2[/tex]

Which statement best describes the polynomial?

A. It is not in standard form because the degree of the first term is not greater than six.
B. It is not in standard form because the degree of the first term should be equal to zero.
C. It is in standard form because the exponents are in order from highest to lowest.
D. It is in standard form because the coefficients are in order from highest to lowest.



Answer :

GinnyAnswer
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]

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