Question

question 13 (multiple choice worth 5 points) (02.01r ) factor $2x^2 - 4x - 30$ completely. $2(x - 3)(x + 5)$ $(2x + 3)(x - 5)$ $2(x - 5)(x + 3)$ $(2x - 5)(x + 3)$

Explanation:

Step1: Factor out the GCF

The given quadratic is \(2x^2 - 4x - 30\). The greatest common factor (GCF) of the terms \(2x^2\), \(-4x\), and \(-30\) is 2. So, factor out 2:
\(2(x^2 - 2x - 15)\)

Step2: Factor the quadratic trinomial

Now, factor \(x^2 - 2x - 15\). We need two numbers that multiply to \(-15\) and add to \(-2\). The numbers are \(-5\) and \(3\) (since \(-5 \times 3 = -15\) and \(-5 + 3 = -2\)). Thus,
\(x^2 - 2x - 15 = (x - 5)(x + 3)\)

Step3: Combine the factors

Substitute the factored trinomial back into the expression from Step 1:
\(2(x - 5)(x + 3)\)

Answer:

\(2(x - 5)(x + 3)\) (the third option: \(2(x - 5)(x + 3)\))