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Answer :
- Identify the exponents of each term in the polynomial.
- Arrange the terms in decreasing order of their exponents.
- The polynomial in descending order is $4x^{11} + x^7 + 3x^3 - 5x + 9$.
- The correct option is B. $\boxed{4 x^{11}+x^7+3 x^3-5 x+9}$
### Explanation
1. Understanding the Problem
We are given the polynomial $3 x^3-5 x+x^7+9+4 x^{11}$ and asked to rewrite it in descending order, which means arranging the terms from the highest power of $x$ to the lowest.
2. Identifying Exponents
First, let's identify the exponents of $x$ in each term:
- $3x^3$ has an exponent of 3.
- $-5x$ has an exponent of 1.
- $x^7$ has an exponent of 7.
- $9$ is a constant term, which can be thought of as $9x^0$, so it has an exponent of 0.
- $4x^{11}$ has an exponent of 11.
3. Arranging in Descending Order
Now, we arrange the terms in descending order of their exponents. The highest exponent is 11, followed by 7, then 3, then 1, and finally 0. So, the polynomial in descending order is $4x^{11} + x^7 + 3x^3 - 5x + 9$.
4. Finding the Correct Option
Comparing our result with the given options, we see that option B, $4 x^{11}+x^7+3 x^3-5 x+9$, matches our arrangement.
### Examples
Polynomials are used to model various real-world phenomena, such as the trajectory of a ball, the growth of a population, or the behavior of electrical circuits. Arranging polynomials in descending order makes it easier to analyze their behavior and identify key features, such as the leading term and the degree of the polynomial. This is useful in fields like physics, engineering, and economics, where polynomial models are frequently used.
- Arrange the terms in decreasing order of their exponents.
- The polynomial in descending order is $4x^{11} + x^7 + 3x^3 - 5x + 9$.
- The correct option is B. $\boxed{4 x^{11}+x^7+3 x^3-5 x+9}$
### Explanation
1. Understanding the Problem
We are given the polynomial $3 x^3-5 x+x^7+9+4 x^{11}$ and asked to rewrite it in descending order, which means arranging the terms from the highest power of $x$ to the lowest.
2. Identifying Exponents
First, let's identify the exponents of $x$ in each term:
- $3x^3$ has an exponent of 3.
- $-5x$ has an exponent of 1.
- $x^7$ has an exponent of 7.
- $9$ is a constant term, which can be thought of as $9x^0$, so it has an exponent of 0.
- $4x^{11}$ has an exponent of 11.
3. Arranging in Descending Order
Now, we arrange the terms in descending order of their exponents. The highest exponent is 11, followed by 7, then 3, then 1, and finally 0. So, the polynomial in descending order is $4x^{11} + x^7 + 3x^3 - 5x + 9$.
4. Finding the Correct Option
Comparing our result with the given options, we see that option B, $4 x^{11}+x^7+3 x^3-5 x+9$, matches our arrangement.
### Examples
Polynomials are used to model various real-world phenomena, such as the trajectory of a ball, the growth of a population, or the behavior of electrical circuits. Arranging polynomials in descending order makes it easier to analyze their behavior and identify key features, such as the leading term and the degree of the polynomial. This is useful in fields like physics, engineering, and economics, where polynomial models are frequently used.
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