Answer :
To determine which statement best describes the polynomial [tex]\(13y^8 - 4y^7 + 3y\)[/tex], we need to understand what defines a polynomial in standard form.
A polynomial is said to be in standard form when its terms are written in descending order of their exponents.
Let's analyze the given polynomial step-by-step:
1. Identifying Terms and Exponents:
- The terms of the polynomial are [tex]\(13y^8\)[/tex], [tex]\(-4y^7\)[/tex], and [tex]\(3y\)[/tex].
- The exponents of these terms are 8, 7, and 1 respectively.
2. Descending Order of Exponents:
- The exponents in the polynomial are indeed in descending order: 8, 7, and 1.
3. Checking the Statements:
- "It is in standard form because the coefficients are in order from highest to lowest." This is incorrect because coefficients do not determine standard form.
- "It is in standard form because the exponents are in order from highest to lowest." This is correct because the polynomial terms are arranged according to descending exponents, which defines the standard form.
- "It is in standard form because there is no constant." This is incorrect because having no constant term is not a criterion for a polynomial to be in standard form.
- "It is in standard form because the coefficients cannot be further simplified." This is incorrect because the simplification of coefficients does not determine the standard form.
Therefore, the statement that best describes the given polynomial [tex]\(13y^8 - 4y^7 + 3y\)[/tex] is:
It is in standard form because the exponents are in order from highest to lowest.
The correct answer is the second statement.
A polynomial is said to be in standard form when its terms are written in descending order of their exponents.
Let's analyze the given polynomial step-by-step:
1. Identifying Terms and Exponents:
- The terms of the polynomial are [tex]\(13y^8\)[/tex], [tex]\(-4y^7\)[/tex], and [tex]\(3y\)[/tex].
- The exponents of these terms are 8, 7, and 1 respectively.
2. Descending Order of Exponents:
- The exponents in the polynomial are indeed in descending order: 8, 7, and 1.
3. Checking the Statements:
- "It is in standard form because the coefficients are in order from highest to lowest." This is incorrect because coefficients do not determine standard form.
- "It is in standard form because the exponents are in order from highest to lowest." This is correct because the polynomial terms are arranged according to descending exponents, which defines the standard form.
- "It is in standard form because there is no constant." This is incorrect because having no constant term is not a criterion for a polynomial to be in standard form.
- "It is in standard form because the coefficients cannot be further simplified." This is incorrect because the simplification of coefficients does not determine the standard form.
Therefore, the statement that best describes the given polynomial [tex]\(13y^8 - 4y^7 + 3y\)[/tex] is:
It is in standard form because the exponents are in order from highest to lowest.
The correct answer is the second statement.
