Question

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Explanation:

Step1: Identify Beth's error

Check the combination of $-27x^2$ and $-2x^2$. Beth wrote $-29x^2$, but:
$$-27x^2 + (-2x^2) = -29x^2$$
Now check the product of $-9$ and $-x$:
$$(-9) \times (-x) = 9x$$
Beth incorrectly calculated this as $-9x$.

Step2: Calculate the correct polynomial

Sum all correct terms:
$$6x^3 + (-2x^2) + 8x + (-27x^2) + 9x + (-36)$$
Combine like terms for $x^2$:
$$-2x^2 -27x^2 = -29x^2$$
Combine like terms for $x$:
$$8x + 9x = 17x$$
Assemble the full polynomial:
$$6x^3 -29x^2 +17x -36$$

Answer:

1. B. incorrectly multiplied $-x$ and $-9$
2. B. $6x^3 -29x^2 +17x -36$