Answer :
To write the polynomial [tex]\(9x^3 - 6 + 7x^2\)[/tex] in standard form, we need to arrange the terms in order of decreasing degree (highest power of [tex]\(x\)[/tex] first).
Step 1: Arrange by Degree
Identify and reorder the terms from the highest degree to the lowest:
- The term [tex]\(9x^3\)[/tex] has the degree of 3.
- The term [tex]\(7x^2\)[/tex] has the degree of 2.
- The constant term [tex]\(-6\)[/tex] is degree 0 (since there is no [tex]\(x\)[/tex]).
Rearranging these terms in descending order gives us:
[tex]\[9x^3 + 7x^2 - 6\][/tex]
Standard Form:
This rearrangement gives the polynomial in standard form: [tex]\[9x^3 + 7x^2 - 6\][/tex]
Step 2: Classification by Degree
The degree of a polynomial is determined by the highest power of [tex]\(x\)[/tex] in the polynomial. Here, the highest power is 3 (from the term [tex]\(9x^3\)[/tex]).
Classification by Degree:
The polynomial is a cubic polynomial because its degree is 3.
Step 3: Classification by Number of Terms
Count the number of distinct terms:
- [tex]\(9x^3\)[/tex]
- [tex]\(7x^2\)[/tex]
- [tex]\(-6\)[/tex]
There are three terms in this polynomial.
Classification by Number of Terms:
The polynomial is a trinomial because it has three terms.
So, the correct answer choice for the polynomial in standard form is:
C. [tex]\(9x^3 + 7x^2 - 6\)[/tex]
In summary, the polynomial [tex]\(9x^3 + 7x^2 - 6\)[/tex] when written in standard form is classified as a cubic trinomial.
Step 1: Arrange by Degree
Identify and reorder the terms from the highest degree to the lowest:
- The term [tex]\(9x^3\)[/tex] has the degree of 3.
- The term [tex]\(7x^2\)[/tex] has the degree of 2.
- The constant term [tex]\(-6\)[/tex] is degree 0 (since there is no [tex]\(x\)[/tex]).
Rearranging these terms in descending order gives us:
[tex]\[9x^3 + 7x^2 - 6\][/tex]
Standard Form:
This rearrangement gives the polynomial in standard form: [tex]\[9x^3 + 7x^2 - 6\][/tex]
Step 2: Classification by Degree
The degree of a polynomial is determined by the highest power of [tex]\(x\)[/tex] in the polynomial. Here, the highest power is 3 (from the term [tex]\(9x^3\)[/tex]).
Classification by Degree:
The polynomial is a cubic polynomial because its degree is 3.
Step 3: Classification by Number of Terms
Count the number of distinct terms:
- [tex]\(9x^3\)[/tex]
- [tex]\(7x^2\)[/tex]
- [tex]\(-6\)[/tex]
There are three terms in this polynomial.
Classification by Number of Terms:
The polynomial is a trinomial because it has three terms.
So, the correct answer choice for the polynomial in standard form is:
C. [tex]\(9x^3 + 7x^2 - 6\)[/tex]
In summary, the polynomial [tex]\(9x^3 + 7x^2 - 6\)[/tex] when written in standard form is classified as a cubic trinomial.
