Which of the following is incorrectly factored? $$ 3 x^{2}+14 x-49=(3 x-7)(x+7) $$ $$ 4 x^{2}+23 x-6=(4 x-3)(x+2) $$ $$ 6 x^{2}+7 x-24=(2 x-3)(3 x+8) $$ $$ x^{2}-4 x-60=(x+6)(x-10) $$

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Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$x^{2}-4x-60=0$$
- step1: Factor the expression:
  $$\left(x-10\right)\left(x+6\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&x-10=0\&x+6=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=10\&x=-6\end{align}$$
- step4: Rewrite:
  $$x_{1}=-6,x_{2}=10$$
Solve the equation $$ 6 x^{2}+7 x-24=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$6x^{2}+7x-24=0$$
- step1: Factor the expression:
  $$\left(2x-3\right)\left(3x+8\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&2x-3=0\&3x+8=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=\frac{3}{2}\&x=-\frac{8}{3}\end{align}$$
- step4: Rewrite:
  $$x_{1}=-\frac{8}{3},x_{2}=\frac{3}{2}$$
Solve the equation $$ 4 x^{2}+23 x-6=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$4x^{2}+23x-6=0$$
- step1: Factor the expression:
  $$\left(x+6\right)\left(4x-1\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&4x-1=0\&x+6=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=\frac{1}{4}\&x=-6\end{align}$$
- step4: Rewrite:
  $$x_{1}=-6,x_{2}=\frac{1}{4}$$
Solve the equation $$ 3 x^{2}+14 x-49=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$3x^{2}+14x-49=0$$
- step1: Factor the expression:
  $$\left(x+7\right)\left(3x-7\right)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&3x-7=0\&x+7=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=\frac{7}{3}\&x=-7\end{align}$$
- step4: Rewrite:
  $$x_{1}=-7,x_{2}=\frac{7}{3}$$
Let's analyze each of the given factorizations by solving the corresponding quadratic equations and comparing the roots with those obtained from the factorizations.

1. **For $$ 3x^{2}+14x-49=(3x-7)(x+7) $$**:
   - The roots of $$ 3x^{2}+14x-49=0 $$ are:
     - $$ x_{1} = -7 $$
     - $$ x_{2} = \frac{7}{3} $$
   - The factorization $$ (3x-7)(x+7) $$ gives roots:
     - Setting $$ 3x-7=0 $$ gives $$ x=\frac{7}{3} $$
     - Setting $$ x+7=0 $$ gives $$ x=-7 $$
   - This factorization is **correct**.

2. **For $$ 4x^{2}+23x-6=(4x-3)(x+2) $$**:
   - The roots of $$ 4x^{2}+23x-6=0 $$ are:
     - $$ x_{1} = -6 $$
     - $$ x_{2} = \frac{1}{4} $$
   - The factorization $$ (4x-3)(x+2) $$ gives roots:
     - Setting $$ 4x-3=0 $$ gives $$ x=\frac{3}{4} $$
     - Setting $$ x+2=0 $$ gives $$ x=-2 $$
   - This factorization is **incorrect**.

3. **For $$ 6x^{2}+7x-24=(2x-3)(3x+8) $$**:
   - The roots of $$ 6x^{2}+7x-24=0 $$ are:
     - $$ x_{1} = -\frac{8}{3} $$
     - $$ x_{2} = \frac{3}{2} $$
   - The factorization $$ (2x-3)(3x+8) $$ gives roots:
     - Setting $$ 2x-3=0 $$ gives $$ x=\frac{3}{2} $$
     - Setting $$ 3x+8=0 $$ gives $$ x=-\frac{8}{3} $$
   - This factorization is **correct**.

4. **For $$ x^{2}-4x-60=(x+6)(x-10) $$**:
   - The roots of $$ x^{2}-4x-60=0 $$ are:
     - $$ x_{1} = -6 $$
     - $$ x_{2} = 10 $$
   - The factorization $$ (x+6)(x-10) $$ gives roots:
     - Setting $$ x+6=0 $$ gives $$ x=-6 $$
     - Setting $$ x-10=0 $$ gives $$ x=10 $$
   - This factorization is **correct**.

### Conclusion:
The incorrectly factored expression is:
$$
4x^{2}+23x-6=(4x-3)(x+2)
$$
The incorrectly factored expression is $$ 4x^{2}+23x-6=(4x-3)(x+2) $$.

Which of the following is incorrectly factored? \( 3 x^{2}+14 x-49=(3 x-7)(x+7) \) \( 4 x^{2}+23 x-6=(4 x-3)(x+2) \) \( 6 x^{2}+7 x-24=(2 x-3)(3 x+8) \) \( x^{2}-4 x-60=(x+6)(x-10) \)

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