Question

question
factor completely.
$-2x^2 - 18x - 36$

Explanation:

Step1: Factor out the greatest common factor (GCF)

The GCF of \(-2x^2\), \(-18x\), and \(-36\) is \(-2\). So we factor out \(-2\):
\[
-2x^2 - 18x - 36 = -2(x^2 + 9x + 18)
\]

Step2: Factor the quadratic trinomial

We need to factor \(x^2 + 9x + 18\). We look for two numbers that multiply to \(18\) and add up to \(9\). The numbers are \(6\) and \(3\) because \(6\times3 = 18\) and \(6 + 3 = 9\). So we can factor it as:
\[
x^2 + 9x + 18 = (x + 6)(x + 3)
\]

Step3: Combine the factors

Putting it all together, the completely factored form is:
\[
-2(x + 6)(x + 3)
\]

Answer:

\(-2(x + 6)(x + 3)\)