Question

question
factor completely.
$3x^2 - 6x - 105$

Explanation:

Step1: Factor out the greatest common factor (GCF)

The GCF of \(3x^2\), \(-6x\), and \(-105\) is 3. So we factor out 3:
\(3x^2 - 6x - 105 = 3(x^2 - 2x - 35)\)

Step2: Factor the quadratic trinomial

We need to factor \(x^2 - 2x - 35\). We look for two numbers that multiply to \(-35\) and add up to \(-2\). The numbers are \(-7\) and \(5\) because \(-7\times5 = -35\) and \(-7 + 5 = -2\). So we can factor the trinomial as:
\(x^2 - 2x - 35=(x - 7)(x + 5)\)

Step3: Combine the factors

Substituting the factored trinomial back into the expression from Step1, we get:
\(3(x - 7)(x + 5)\)

Answer:

\(3(x - 7)(x + 5)\)