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To find the zeros of the function \( f(x) = (2x + 6)(x - 4) \), we set the function equal to zero and solve for \(x\).

\[
f(x) = 0 \implies (2x + 6)(x - 4) = 0
\]

Using the zero product property, we know that either:

\[
2x + 6 = 0 \quad \text{or} \quad x - 4 = 0
\]

### Solving the first equation:
\[
2x + 6 = 0
\]
Subtract 6 from both sides:
\[
2x = -6
\]
Divide by 2:
\[
x = -3
\]

### Solving the second equation:
\[
x - 4 = 0
\]
Add 4 to both sides:
\[
x = 4
\]

So, the zeros of the function are \(x = -3\) and \(x = 4\).

### The correct answer is **B**.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you apply the zero product property?
2. Can you graph the function and its zeros?
3. What happens to the function values as \(x\) approaches the zeros?
4. How do you factor more complex quadratic functions?
5. What are the properties of the roots of polynomial functions?

**Tip**: Always set each factor equal to zero separately when using the zero product property.

What are the zeros of the function f(x) = (2x + 6)(x - 4)?

Learn how to find the zeros of the factored function f(x) = (2x + 6)(x - 4). This problem uses the zero product property and introduces basic factoring concepts in algebra. Suitable for students in Grades 8-10.

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