Which of the following polynomials can approximate the expression (4x3+5)(3x6−8x2)2x2+4x3+13

Question

using first and last terms only?(1 point)
Responses

4x3+...13

6x7+...−7
6 x superscript 7 baseline plus 13

6x7+...4x3

12x9+...13

Answer 1

To approximate the expression \( (4x^3 + 5)(3x^6 - 8x^2)2x^2 + 4x^3 + 13 \) using only the first and last terms, we need to identify the leading term from each polynomial and the constant term.

1. From the first polynomial \( 4x^3 + 5 \), the leading term is \( 4x^3 \).
2. From the second polynomial \( 3x^6 - 8x^2 \), the leading term is \( 3x^6 \).
3. The constant term at the end of the expression is 13.

Now, we can find the leading term of the product \( (4x^3)(3x^6) \):

• The leading term will be \( 4x^3 \cdot 3x^6 = 12x^9 \).

Thus, the approximate expression using only the first and last terms is: \[ 12x^9 + 13 \]

Therefore, the correct choice is: 12x9 + ... 13.