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.
