Question

5x^2 + 10x - 15

Explanation:

Factor out the greatest common factor

Using the Greatest Common Factor knowledge point, we find the largest common factor of the terms \(5x^2\), \(10x\), and \(-15\), which is \(5\).

$$ 5x^2 + 10x - 15 = 5(x^2 + 2x - 3) $$

Factor the remaining quadratic trinomial

Using the Polynomial Factoring knowledge point, we find two numbers that multiply to \(-3\) and add to \(2\). These numbers are \(3\) and \(-1\).

$$ x^2 + 2x - 3 = (x + 3)(x - 1) $$

Write the fully factored expression

We combine the factored parts to write the final expression.

$$ 5(x + 3)(x - 1) $$

Answer:

\(5(x + 3)(x - 1)\)