Factor the polynomial.
$x^2-2x-15$

• A. $\(\left\)(x-3\(\right\))\(\left\)(x-5\(\right\))$
• B. $\(\left\)(x-3\(\right\))\(\left\)(x+5\(\right\))$
• C. $\(\left\)(x+3\(\right\))\(\left\)(x-5\(\right\))$
• D. $\(\left\)(x+3\(\right\))\(\left\)(x+5\(\right\))$

Answer: (C)

Verified step by step guidance

1. Identify the polynomial to be factored: \(x^2 - 2x - 15\).
2. Look for two numbers that multiply to the constant term (-15) and add to the linear coefficient (-2).
3. The numbers that satisfy these conditions are 3 and -5, because 3 * (-5) = -15 and 3 + (-5) = -2.
4. Rewrite the middle term (-2x) using the numbers found: \(x^2 + 3x - 5x - 15\).
5. Factor by grouping: Group the terms as \((x^2 + 3x) + (-5x - 15)\), then factor out the common factors to get \((x + 3)(x - 5)\).