Question

divide using long division.

\\((3x^5 - x^3 - 5x^2 - 5x + 10) \div (x^2 - 2)\\)

a. \\(3x^3 + 5x + 5 + \frac{5x}{x^2 - 2}\\)

b. \\(3x^3 + 5x - 5 + \frac{5x + 20}{x^2 - 2}\\)

c. \\(3x^3 + 5x - 5 - \frac{5x}{x^2 - 2}\\)

d. \\(3x^3 + 5x - 5 + \frac{5x}{x^2 - 2}\\)

Explanation:

Set up the division with placeholders

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK0
$$

Divide the leading terms to find the quotient

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK1
$$

Continue the division process

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK2
$$

Find the final quotient term and remainder

Using the Polynomial Long Division knowledge point

$$
LATEXBLOCK3
$$

Express the final result

Using the Polynomial Long Division knowledge point

$$ 3x^3 + 5x - 5 + \frac{5x}{x^2 - 2} $$

Answer:

• A. \(3x^3 + 5x + 5 + \frac{5x}{x^2 - 2}\)
• B. \(3x^3 + 5x - 5 + \frac{5x + 20}{x^2 - 2}\)
• C. \(3x^3 + 5x - 5 - \frac{5x}{x^2 - 2}\)
• D. \(3x^3 + 5x - 5 + \frac{5x}{x^2 - 2}\) (Correct answer)