Question

one root of \\(f(x) = x^3 + 10x^2 - 25x - 250\\) is \\(x = -10\\). what are all the roots of the function? use the remainder theorem.

\\(x = -25\\) or \\(x = 10\\)
\\(x = -25, x = 1,\\) or \\(x = 10\\)
\\(x = -10\\) or \\(x = 5\\)
\\(x = -10, x = -5,\\) or \\(x = 5\\)

Explanation:

Verify the given root

Using the Remainder Theorem knowledge point

$$
LATEXBLOCK0
$$

Factor the polynomial

Using the Polynomial Factoring knowledge point

$$
LATEXBLOCK1
$$

Find all roots

Using the Polynomial Roots knowledge point

$$
LATEXBLOCK2
$$

Answer:

• \(x = -25\) or \(x = 10\)
• \(x = -25\), \(x = 1, \text{ or } x = 10\)
• \(x = -10\) or \(x = 5\)
• \(x = -10\), \(x = -5, \text{ or } x = 5\) (Correct answer)