Which statement best describes the polynomial?

[tex]\[ 6 - 8y + 14y^7 + 16y^8 \][/tex]

A. It is in standard form because the exponents are in order from lowest to highest.
B. It is in standard form because the coefficients are in order from lowest to highest.
C. It is not in standard form because the exponents are not in order from highest to lowest.
D. It is not in standard form because it can be further simplified.



Answer :

Let's analyze the given polynomial:

[tex]\[ 6 - 8y + 14y^7 + 16y^8 \][/tex]

To determine whether it is in standard form, let's recall that in standard form, a polynomial must have its terms ordered by the exponents of the variable in descending order (from highest to lowest exponent).

1. Identify the exponents:
- The exponent of [tex]\(6\)[/tex] is [tex]\(0\)[/tex] (since it can be seen as [tex]\(6y^0\)[/tex]).
- The exponent of [tex]\(-8y\)[/tex] is [tex]\(1\)[/tex].
- The exponent of [tex]\(14y^7\)[/tex] is [tex]\(7\)[/tex].
- The exponent of [tex]\(16y^8\)[/tex] is [tex]\(8\)[/tex].

2. Order of exponents:
- The polynomial should be ordered from the highest exponent to the lowest exponent. That is:

[tex]\[ 16y^8 + 14y^7 - 8y + 6 \][/tex]

3. Check the given polynomial:
- The given polynomial is [tex]\(6 - 8y + 14y^7 + 16y^8\)[/tex].

Comparing the given polynomial with the standard form order, we can see that:

- The highest exponent term [tex]\(16y^8\)[/tex] should come first.
- Then, the next highest exponent term [tex]\(14y^7\)[/tex].
- Followed by the [tex]\(-8y\)[/tex] term.
- And lastly, the constant term [tex]\(6\)[/tex].

Since the exponents are not in descending order in the given polynomial [tex]\(6 - 8y + 14y^7 + 16y^8\)[/tex], we can conclude:

- It is not in standard form because the exponents are not in order from highest to lowest.

Thus, the statement that best describes the polynomial is:

It is not in standard form because the exponents are not in order from highest to lowest.