Which statement is true about the equation (*x* – 4)(*x* + 2) = 16? 

The equation *x* – 4 = 16 can be used to solve for a solution of the given equation.

The standard form of the equation is *x*2 – 2*x* – 8 = 0.

The factored form of the equation is (*x* + 4)(*x* – 6) = 0.

One solution of the equation is *x* = –6.

Let's analyze each of the given statements to determine which one is true about the equation \((x - 4)(x + 2) = 16\).

### Step 1: Expanding the equation
Expand the left-hand side of the equation:
\[
(x - 4)(x + 2) = x^2 + 2x - 4x - 8 = x^2 - 2x - 8
\]
Thus, the equation becomes:
\[
x^2 - 2x - 8 = 16
\]
Now, subtract 16 from both sides to bring it to standard form:
\[
x^2 - 2x - 8 - 16 = 0
\]
This simplifies to:
\[
x^2 - 2x - 24 = 0
\]
### Step 2: Analyzing the statements
Now we can evaluate each statement:

1. **"The equation \(x - 4 = 16\) can be used to solve for a solution of the given equation."**  
   This is **false**. Solving \(x - 4 = 16\) yields \(x = 20\), but substituting \(x = 20\) into the original equation doesn't satisfy it.

2. **"The standard form of the equation is \(x^2 - 2x - 8 = 0\)."**  
   This is **false**. As shown above, the correct standard form is \(x^2 - 2x - 24 = 0\), not \(x^2 - 2x - 8 = 0\).

3. **"The factored form of the equation is \((x + 4)(x - 6) = 0\)."**  
   Let's factor \(x^2 - 2x - 24 = 0\):
   \[
   (x - 6)(x + 4) = 0
   \]
   This is **true**.

4. **"One solution of the equation is \(x = -6\)."**  
   From the factored form \((x - 6)(x + 4) = 0\), the solutions are \(x = 6\) and \(x = -4\), not \(x = -6\).  
   This is **false**.

### Conclusion:
The correct statement is:
- **"The factored form of the equation is \((x + 4)(x - 6) = 0\)."**

Would you like more details or have any other questions?

### 5 Related Questions:
1. How do you solve a quadratic equation by factoring?
2. What are the different methods to solve quadratic equations?
3. Can you explain the relationship between the standard form and the factored form of a quadratic equation?
4. How do you check if a solution to an equation is correct?
5. Why is factoring useful in solving quadratic equations?

### Tip:
Always check your solutions by substituting them back into the original equation to verify if they satisfy the equation.

Which statement is true about the equation (x – 4)(x + 2) = 16?

- The equation x – 4 = 16 can be used to solve for a solution of the given equation.
- The standard form of the equation is x^2 – 2x – 8 = 0.
- The factored form of the equation is (x + 4)(x – 6) = 0.
- One solution of the equation is x = –6.

Learn how to solve the quadratic equation (x - 4)(x + 2) = 16 using factoring techniques. This detailed explanation breaks down the equation into its standard form, shows the correct factored form, and verifies which statements about the equation are true. Suitable for students in Grades 8-10.

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