Question

Identify each factor of 2x2−4x−16
.

2

4

2x

x−8

x−4

x−2

x+2

x+4

Answer 1

To factor the expression \(2x^2 - 4x - 16\), we can start by factoring out the common factor, which is \(2\):

\[
2(x^2 - 2x - 8)
\]

Next, we need to factor the quadratic \(x^2 - 2x - 8\). We are looking for two numbers that multiply to \(-8\) (the constant term) and add to \(-2\) (the coefficient of the linear term). These two numbers are \(-4\) and \(2\).

So we can factor the quadratic as follows:

\[
x^2 - 2x - 8 = (x - 4)(x + 2)
\]

Putting it all together, we have:

\[
2(x^2 - 2x - 8) = 2(x - 4)(x + 2)
\]

Thus, the complete factorization of \(2x^2 - 4x - 16\) is:

\[
2(x - 4)(x + 2)
\]

Now, let's identify the factors from the options you provided:

- 2 (this is a factor)
- 4 (not a factor)
- \(2x\) (not a factor)
- \(x - 8\) (not a factor)
- \(x - 4\) (this is a factor)
- \(x - 2\) (not a factor)
- \(x + 2\) (this is a factor)
- \(x + 4\) (not a factor)

The identified factors of \(2x^2 - 4x - 16\) are \(2\), \(x - 4\), and \(x + 2\).