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Answer :
To write the polynomial [tex]\(10x^7 - 9x^2 + 15x^3 + 9\)[/tex] in standard form, we need to arrange all terms in descending order based on their exponents or powers of [tex]\(x\)[/tex]. Here's how you can do it step-by-step:
1. Identify the terms: The given polynomial consists of four terms:
- [tex]\(10x^7\)[/tex]
- [tex]\(-9x^2\)[/tex]
- [tex]\(15x^3\)[/tex]
- [tex]\(9\)[/tex] (which can be thought of as [tex]\(9x^0\)[/tex] since any number to the power of 0 is 1)
2. Order by exponents: List the terms in order from the highest exponent of [tex]\(x\)[/tex] to the lowest. In this case:
- The highest exponent is 7 in the term [tex]\(10x^7\)[/tex].
- The next highest is 3 in the term [tex]\(15x^3\)[/tex].
- The next is 2 in the term [tex]\(-9x^2\)[/tex].
- The constant term [tex]\(9\)[/tex] can be considered as the lowest exponent (0).
3. Write the polynomial in standard form: Arrange the terms you've identified in descending order of their exponents:
[tex]\[10x^7 + 15x^3 - 9x^2 + 9\][/tex]
By following these steps, the polynomial [tex]\(10x^7 - 9x^2 + 15x^3 + 9\)[/tex] in standard form is:
[tex]\[10x^7 + 15x^3 - 9x^2 + 9\][/tex]
1. Identify the terms: The given polynomial consists of four terms:
- [tex]\(10x^7\)[/tex]
- [tex]\(-9x^2\)[/tex]
- [tex]\(15x^3\)[/tex]
- [tex]\(9\)[/tex] (which can be thought of as [tex]\(9x^0\)[/tex] since any number to the power of 0 is 1)
2. Order by exponents: List the terms in order from the highest exponent of [tex]\(x\)[/tex] to the lowest. In this case:
- The highest exponent is 7 in the term [tex]\(10x^7\)[/tex].
- The next highest is 3 in the term [tex]\(15x^3\)[/tex].
- The next is 2 in the term [tex]\(-9x^2\)[/tex].
- The constant term [tex]\(9\)[/tex] can be considered as the lowest exponent (0).
3. Write the polynomial in standard form: Arrange the terms you've identified in descending order of their exponents:
[tex]\[10x^7 + 15x^3 - 9x^2 + 9\][/tex]
By following these steps, the polynomial [tex]\(10x^7 - 9x^2 + 15x^3 + 9\)[/tex] in standard form is:
[tex]\[10x^7 + 15x^3 - 9x^2 + 9\][/tex]
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