Question

question 3 of 5

select the correct answer.

one factor of this polynomial is \\( (x + 8) \\).
\\ x^3 + 5x^2 - 11x + 104 \\

use synthetic division to find the other factor of the polynomial.

\\( \bigcirc x^3 - 3x^2 + 13x \\)
\\( \bigcirc x^2 - 3x + 13 \\)
\\( \bigcirc x^2 + 3x + 13 \\)
\\( \bigcirc x^3 + 3x^2 + 13x \\)

Explanation:

Set up synthetic division with root \(c = -8\)

$$
LATEXBLOCK0
$$

Write the quotient polynomial

$$ q(x) = 1x^2 - 3x + 13 = x^2 - 3x + 13 $$

Answer:

• (A) \(x^3 - 3x^2 + 13x\)
• (B) \(x^2 - 3x + 13\) (Correct answer)
• (C) \(x^2 + 3x + 13\)
• (D) \(x^3 + 3x^2 + 13x\)