Choose the correct answer in each drop-down list to complete the factorization: $$ x^{2}-4 x-12=(x- $$ Select $$ -\vee)(x- $$ Select $$ -\vee) $$ $$ 4 x^{2}+11 x-20=(- $$ Select $$ -\vee-5)(- $$ Select $$ -\vee+4) $$ $$ 3 x^{2}+2 x-16=(3 x- $$ Select $$ -\vee)(x- $$ Select $$ -\vee) $$

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Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$x^{2}-4x-12=0$$
- step1: Factor the expression:
  $$\left(x-6\right)\left(x+2\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&x-6=0\&x+2=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=6\&x=-2\end{align}$$
- step4: Rewrite:
  $$x_{1}=-2,x_{2}=6$$
Solve the equation $$ 3 x^{2}+2 x-16=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$3x^{2}+2x-16=0$$
- step1: Factor the expression:
  $$\left(x-2\right)\left(3x+8\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&x-2=0\&3x+8=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=2\&x=-\frac{8}{3}\end{align}$$
- step4: Rewrite:
  $$x_{1}=-\frac{8}{3},x_{2}=2$$
Solve the equation $$ 4 x^{2}+11 x-20=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$4x^{2}+11x-20=0$$
- step1: Factor the expression:
  $$\left(x+4\right)\left(4x-5\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&4x-5=0\&x+4=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=\frac{5}{4}\&x=-4\end{align}$$
- step4: Rewrite:
  $$x_{1}=-4,x_{2}=\frac{5}{4}$$
Let's solve each factorization step by step.

1. **For the equation $$ x^{2}-4x-12=0 $$**:
   - The roots are $$ x_{1} = -2 $$ and $$ x_{2} = 6 $$.
   - Therefore, the factorization is:
     $$
     x^{2}-4x-12 = (x - (-2))(x - 6) = (x + 2)(x - 6)
     $$

2. **For the equation $$ 4x^{2}+11x-20=0 $$**:
   - The roots are $$ x_{1} = -4 $$ and $$ x_{2} = \frac{5}{4} $$ (or $$ 1.25 $$).
   - Therefore, the factorization is:
     $$
     4x^{2}+11x-20 = (4x - (-4))(4x - \frac{5}{4}) = (4x + 4)(4x - 5)
     $$

3. **For the equation $$ 3x^{2}+2x-16=0 $$**:
   - The roots are $$ x_{1} = -\frac{8}{3} $$ and $$ x_{2} = 2 $$.
   - Therefore, the factorization is:
     $$
     3x^{2}+2x-16 = (3x - (-\frac{8}{3}))(x - 2) = (3x + \frac{8}{3})(x - 2)
     $$

Now, let's fill in the blanks:

1. $$ x^{2}-4x-12=(x+2)(x-6) $$
2. $$ 4x^{2}+11x-20=(4x+4)(4x-5) $$
3. $$ 3x^{2}+2x-16=(3x+\frac{8}{3})(x-2) $$

So the completed factorization is:
- $$ x^{2}-4x-12=(x+2)(x-6) $$
- $$ 4x^{2}+11x-20=(4x+4)(4x-5) $$
- $$ 3x^{2}+2x-16=(3x+\frac{8}{3})(x-2) $$
$$ x^{2}-4x-12=(x+2)(x-6) $$, $$ 4x^{2}+11x-20=(4x+4)(4x-5) $$, $$ 3x^{2}+2x-16=(3x+\frac{8}{3})(x-2) $$.

Choose the correct answer in each drop-down list to complete the
factorization:
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