Question

anja divides \\( (8x^3 - 36x^2 + 54x - 27) \\) by \\( (2x - 3) \\) as shown below. what error does anja make?

\\
\

$$\begin{array}{r} 4x^2 - 12x + 9 \\\\ 2x - 3 \\overline{\\smash{\\big)} 8x^3 - 36x^2 + 54x - 27} \\\\ \\underline{8x^3 - 12x^2} \\phantom{-27} \\\\ -24x^2 + 54x \\phantom{-27} \\\\ \\underline{-24x^2 + 36x} \\phantom{-27} \\\\ 18x - 27 \\\\ \\underline{18x + 27} \\\\ -54 \\\\ \\end{array}$$

\\

• she makes a subtraction error.
• she makes an error choosing the x-term in the quotient.
• she makes a multiplication error.
• she makes an error rewriting the problem in long division.

Explanation:

Analyze the first division step

Using the Polynomial Division knowledge point

$$
LATEXBLOCK0
$$

Analyze the second division step

Using the Polynomial Division knowledge point

$$
LATEXBLOCK1
$$

Analyze the third division step

Using the Polynomial Division knowledge point

$$
LATEXBLOCK2
$$

Identify the error in Anja's work

Using the Polynomial Division knowledge point
Anja's third subtraction step shows:

$$
LATEXBLOCK3
$$

This is a multiplication error.

Answer:

• She makes a subtraction error.
• She makes an error choosing the x-term in the quotient.
• She makes a multiplication error. (Correct answer)
• She makes an error rewriting the problem in long division.