Let's analyze each step in detail to identify where the mistake might have occurred in simplifying the polynomial expression [tex]\((6x^3 + 8x^2 - 7x) - (2x^2 + 3)(x - 8)\)[/tex].
### Step 1
First, expand [tex]\((2x^2 + 3)(x - 8)\)[/tex]:
[tex]\[
(2x^2 + 3)(x - 8) = 2x^2 \cdot x + 2x^2 \cdot (-8) + 3 \cdot x + 3 \cdot (-8)
\][/tex]
[tex]\[
= 2x^3 - 16x^2 + 3x - 24
\][/tex]
Now the expression becomes:
[tex]\[
(6x^3 + 8x^2 - 7x) - (2x^3 - 16x^2 + 3x - 24)
\][/tex]
Kalid correctly expanded the expression and then wrote:
[tex]\[
\left(6 x^3 + 8 x^2 - 7 x\right) - \left(2 x^3 - 16 x^2 + 3 x - 24\right)
\][/tex]
Therefore, Kalid's Step 1 is correct.
### Step 2
Distribute the negative sign and combine like terms:
[tex]\[
6x^3 + 8x^2 - 7x - 2x^3 + 16x^2 - 3x + 24
\][/tex]
Combine like terms:
[tex]\[
(6x^3 - 2x^3) + (8x^2 + 16x^2) + (-7x - 3x) + 24
\][/tex]
[tex]\[
= 4x^3 + 24x^2 - 10x + 24
\][/tex]
After examining Kalid's Step 2:
[tex]\[
6 x^3 + 8 x^2 - 7 x - 2 x^3 + 16 x^2 - 3 x - 24
\][/tex]
It appears he did not combine the constants correctly, as the last term should be [tex]\(+24\)[/tex] (positive) instead of [tex]\(-24\)[/tex] (negative). Therefore, Kalid made a mistake here.
### Step 3
Kalid's Step 3 gives:
[tex]\[
4 x^3 - 8 x^2 - 4 x - 24
\][/tex]
But from our corrected combination in Step 2, we get:
[tex]\[
4x^3 + 24x^2 - 10x + 24
\][/tex]
Therefore, something is definitely off given that the constants diverged in two different ways.
To maximize surprise, I can conclude that Kalid combined the constants incorrectly between Step 2 and 3. Factoring out the full expression with correct terms will still highlight the mistake in Step 1 cleanup for distribution.
### Conclusion
Kalid made a mistake in Step 2 when combining the constants. Thus, the correct answer is:
B. Step 2.
