Question

when simplified which expressions produce the trinomial 4x^2 - 20x - 24? select the two that apply

Answer 1

To produce the trinomial \(4x^2 - 20x - 24\), we can factor it first.

1. **Factor out the GCF**:

The greatest common factor (GCF) of the coefficients \(4\), \(-20\), and \(-24\) is \(4\). Let's factor that out first:

\[
4(x^2 - 5x - 6)
\]

2. **Factor the quadratic trinomial**:

Now, we will factor \(x^2 - 5x - 6\). We need two numbers that multiply to \(-6\) and add to \(-5\). The numbers \(-6\) and \(1\) fit this criteria.

Thus, we can factor it as:

\[
(x - 6)(x + 1)
\]

3. **Combine all parts**:

So, the original trinomial factors into:

\[
4(x - 6)(x + 1)
\]

Now, from this, the expressions that produce the trinomial \(4x^2 - 20x - 24\) include:

1. \(4(x - 6)(x + 1)\)
2. \((2x - 12)(2x + 2)\) [this does actually distribute to the original trinomial]

To conclude, you should select the two forms \(4(x - 6)(x + 1)\) and \( (2x - 12)(2x + 2) \) as they will yield the same trinomial when simplified.