Question

select the correct answer.

using synthetic division, what is the factored form of this polynomial?
\\x^4 + 6x^3 + 33x^2 + 150x + 200\\

\\((x - 2)(x - 4)(x - 5)(x + 5)\\)
\\((x - 2)(x - 4)(x^2 + 25)\\)
\\((x + 2)(x + 4)(x - 5)(x + 5)\\)
\\((x + 2)(x + 4)(x^2 + 25)\\)

Explanation:

Evaluate the polynomial at potential roots

$$
LATEXBLOCK0
$$

Perform synthetic division by \(x + 2\)

$$
LATEXBLOCK1
$$

$$ Q_1(x) = x^3 + 4x^2 + 25x + 100 $$

Perform synthetic division by \(x + 4\)

$$
LATEXBLOCK2
$$

$$ Q_2(x) = x^2 + 25 $$

Answer:

• (A) \((x - 2)(x - 4)(x - 5)(x + 5)\)
• (B) \((x - 2)(x - 4)(x^2 + 25)\)
• (C) \((x + 2)(x + 4)(x - 5)(x + 5)\)
• (D) \((x + 2)(x + 4)(x^2 + 25)\) (Correct answer)