Question

select the correct answer.

using synthetic division, find \\((2x^4 - 3x^3 - 20x - 21) \div (x - 3)\\).

\\(2x^3 + 3x^2 + 9x + 7\\)
\\(2x^4 + 3x^3 + 9x^2 + 7x\\)
\\(2x^4 + 3x^2 - 11x - 54\\)
\\(2x^3 + 3x^2 - 11x - 54\\)

Explanation:

Set up the synthetic division coefficients

$$
LATEXBLOCK0
$$

Write the resulting quotient polynomial

$$ \text{Quotient} = 2x^3 + 3x^2 + 9x + 7 $$

Answer:

• (A) \(2x^3 + 3x^2 + 9x + 7\) (Correct answer)
• (B) \(2x^4 + 3x^3 + 9x^2 + 7x\)
• (C) \(2x^4 + 3x^2 - 11x - 54\)
• (D) \(2x^3 + 3x^2 - 11x - 54\)