Questions: Factor completely. -2 x^2 -16 x -24

Solution Steps

To factor the quadratic expression completely, first look for a common factor in all the terms. Then, factor the quadratic expression using techniques such as grouping or the quadratic formula if necessary.

We start with the quadratic expression: \[ -2x^2 - 16x - 24 \]

First, we notice that each term in the expression has a common factor of \(-2\). We factor this out: \[ -2(x^2 + 8x + 12) \]

Next, we need to factor the quadratic expression \(x^2 + 8x + 12\). We look for two numbers that multiply to \(12\) and add to \(8\). The numbers \(2\) and \(6\) satisfy these conditions. Thus, we can factor the quadratic as: \[ x^2 + 8x + 12 = (x + 2)(x + 6) \]

Now, substituting back into our expression, we have: \[ -2(x + 2)(x + 6) \]

Final Answer