Which of the following polynomials can approximate the expression (4x3+5)(3x6−8x2)2x2+4x3+13 using first and last terms only?(1 point)

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

1. **Identifying the first term:**
- The first term in the expression \((4x^3 + 5)(3x^6 - 8x^2)\) comes from multiplying the leading terms of each polynomial:
\[
4x^3 \cdot 3x^6 = 12x^{9}.
\]
- Therefore, the leading term of the whole expression will begin with \(12x^9\).

2. **Identifying the last term:**
- The last term is the constant term in the expression. The constant term from \((4x^3 + 5)(3x^6 - 8x^2)\) arises when we consider the constants in both polynomials:
\[
5 \cdot (-8x^2) = -40x^2, \text{ but since the constant term with no }x \text{ must be calculated, we only get } 5 \cdot 3 = 15 \text{ and }\]
\[
(4x^3 \cdot 0) + (5 \cdot 0) = 0 \Rightarrow \text{ so constant term from polynomial } (3x^6)(4x^3) + last constant term = 15 \text{ and }
\]
\[
0 + 15 + 13 \text{ gives } 28.
\]
Therefore, the last (constant) term overall of the expression is \(28\).

3. **Putting it together:**
- From our evaluation, the leading term is \(12x^9\) and the constant term is \(28\).

So, we can approximate the expression using the polynomial that contains just the first and last terms:

\[
\boxed{12x^9 + 28}.
\]