Question

select the correct answer.

lorie is using long division to find the quotient of \\(x^3 + 6x^2 + 5\\) and \\(x^2 + x - 1\\), as shown.

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$$\begin{array}{r} x + 5 - \\frac{4x}{x^2 + x - 1} \\\\ x^2 + x - 1 \\overline{\\smash{)} \\, x^3 + 6x^2 + 0x + 5} \\\\ \\underline{-(x^3 + x^2 - x)} \\hphantom{+ 5} \\\\ 5x^2 + x + 5 \\\\ \\underline{-(5x^2 + 5x - 5)} \\\\ -4x + 0 \\\\ \\end{array}$$

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what mistake did lorie make?

• she added an extra term to the dividend.
• she combined the constants incorrectly in the last step.
• the second term in the quotient should be 7.
• the last term in the quotient has an incorrect denominator.

Explanation:

Perform the first subtraction step in the division

$$ (x^3 + 6x^2 + 0x + 5) - (x^3 + x^2 - x) = 5x^2 + x + 5 $$

Perform the second subtraction step in the division

$$ (5x^2 + x + 5) - (5x^2 + 5x - 5) = -4x + 10 $$

Compare the result with Lorie's work

$$
LATEXBLOCK0
$$

Answer:

• She added an extra term to the dividend.
• She combined the constants incorrectly in the last step. (Correct answer)
• The second term in the quotient should be 7.
• The last term in the quotient has an incorrect denominator.