Which of the following polynomials can approximate the expression (4x3+5)(3x6−8x2)2x2+4x3+13 using first and last terms only?(1 point) Responses 12x9+...13 12 x superscript 7 baseline minus 27 6x7+...−7 6 x superscript 7 baseline plus 13 4x3+...13 6x7+...4x3

To approximate the expression \( (4x^3 + 5)(3x^6 - 8x^2) + 2x^2 + 4x^3 + 13 \) using only the first and last terms, we should identify the first and last terms of each component.

1. The first term of \( 4x^3 + 5 \) is \( 4x^3 \).
2. The first term of \( 3x^6 - 8x^2 \) is \( 3x^6 \).
3. The product of the first terms gives:
\[
(4x^3)(3x^6) = 12x^9
\]

4. The last term of the entire expression \( 2x^2 + 4x^3 + 13 \) is \( 13 \).

So, combining these, the polynomial that best approximates the expression using the first and last terms is:

\[
12x^9 + 13
\]

Thus, the correct polynomial from the given options is:

**12x⁹ + ... + 13**.