Question
Which of the following polynomials can approximate the expression (4x3+5)(3x6−8x2)2x2+4x3+13
using the first and last terms only?(1 point)
Responses
6x7+...−7
6x7+...4x3
12x9+...13
4x3+...13
using the first and last terms only?(1 point)
Responses
6x7+...−7
6x7+...4x3
12x9+...13
4x3+...13
Answers
GPT-4o mini
To approximate the expression \((4x^3 + 5)(3x^6 - 8x^2)2x^2 + 4x^3 + 13\) using the first and last terms only, we can follow these steps:
1. Identify the first term from the first polynomial: \(4x^3\).
2. Identify the first term from the second polynomial: \(3x^6\).
3. The first term of the product \((4x^3)(3x^6) = 12x^9\).
4. Identify the last term in the entire expression, which is \(13\).
Now, we can summarize this as:
- The leading term of the product gives us \(12x^9\).
- The last term of the entire expression gives us \(13\).
Thus, the expression can be approximated as \(12x^9 + ... + 13\).
Therefore, the correct response among the given options is:
**12x9 + ... + 13**.
1. Identify the first term from the first polynomial: \(4x^3\).
2. Identify the first term from the second polynomial: \(3x^6\).
3. The first term of the product \((4x^3)(3x^6) = 12x^9\).
4. Identify the last term in the entire expression, which is \(13\).
Now, we can summarize this as:
- The leading term of the product gives us \(12x^9\).
- The last term of the entire expression gives us \(13\).
Thus, the expression can be approximated as \(12x^9 + ... + 13\).
Therefore, the correct response among the given options is:
**12x9 + ... + 13**.