Question

question 11 (2 points)

determine one of the roots of the following:

\\x^8 - 256\\

16
2
3
4

Explanation:

Set the expression to zero

Using the Polynomial Factoring knowledge point

$$ x^8 - 256 = 0 $$

Factor as a difference of squares

Using the Polynomial Factoring knowledge point

$$ (x^4 - 16)(x^4 + 16) = 0 $$

Factor the real-valued difference of squares

Using the Polynomial Factoring knowledge point

$$ (x^2 - 4)(x^2 + 4)(x^4 + 16) = 0 $$

Factor completely to find real roots

Using the Polynomial Factoring knowledge point

$$ (x - 2)(x + 2)(x^2 + 4)(x^4 + 16) = 0 $$

Solve for the real roots

Using the Polynomial Factoring knowledge point

$$
LATEXBLOCK0
$$

Answer:

• (A) 16
• (B) 2 (Correct answer)
• (C) 3
• (D) 4