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.