Question

select the correct answer.

using synthetic division, find \\((2x^4 + 4x^3 + 2x^2 + 8x + 8) \div (x + 2)\\).

\\(\bigcirc 2x^3 + 2x + 4\\)

\\(\bigcirc 2x^4 + 2x^2 + 4x\\)

\\(\bigcirc 2x^3 + 2x + 4 + \frac{1}{x + 2}\\)

\\(\bigcirc 2x^3 + 2x^2 + 4\\)

Explanation:

Set up the synthetic division table

$$
LATEXBLOCK0
$$

Interpret the resulting coefficients

$$ \text{Quotient} = 2x^3 + 0x^2 + 2x + 4 = 2x^3 + 2x + 4 $$

$$ \text{Remainder} = 0 $$

Match with the given options

$$ (2x^4 + 4x^3 + 2x^2 + 8x + 8) \div (x + 2) = 2x^3 + 2x + 4 $$

Answer:

• (A) \(2x^3 + 2x + 4\) (Correct answer)
• (B) \(2x^4 + 2x^2 + 4x\)
• (C) \(2x^3 + 2x + 4 + \frac{1}{x+2}\)
• (D) \(2x^3 + 2x^2 + 4\)