Question

use synthetic division to find all the possible factors of this polynomial.

(p(x) = x^4 + 4x^3 - 7x^2 - 22x + 24)

select all the correct expressions in the table. for help, see this worked example.

\

$$\begin{tabular}{|c|c|c|} \\hline (x - 1) & (x + 1) & (x - 2) \\\\ \\hline (x + 2) & (x - 3) & (x + 3) \\\\ \\hline (x - 4) & (x + 4) & (x - 6) \\\\ \\hline \\end{tabular}$$

Explanation:

Test potential integer roots using the Factor Theorem

$$
LATEXBLOCK0
$$

Perform synthetic division to find remaining factors

$$
LATEXBLOCK1
$$

$$
LATEXBLOCK2
$$

$$ q(x) = x^2 + 7x + 12 $$

Factor the remaining quadratic expression

$$
LATEXBLOCK3
$$

Answer:

The correct factors of the polynomial from the table are:

• \(x - 1\)
• \(x - 2\)
• \(x + 3\)
• \(x + 4\)