Suppose 
f
(
x
)
=
(
x
−
5
)
(
x
+
4
)
.

Solve 
(
x
−
5
)
(
x
+
4
)
=
0
 for 
x
.

We are given the equation:

\[
(x - 5)(x + 4) = 0
\]

To solve this, we can use the **Zero Product Property**, which states that if the product of two factors is zero, then at least one of the factors must be zero. This gives us two cases to solve for \(x\):

### Case 1: \(x - 5 = 0\)
\[
x = 5
\]

### Case 2: \(x + 4 = 0\)
\[
x = -4
\]

### Solution:
The solutions to the equation are:
\[
x = 5 \quad \text{or} \quad x = -4
\]

Would you like more details on the solution process, or do you have any questions?

Here are 5 related questions:
1. How do you graph \(f(x) = (x - 5)(x + 4)\)?
2. What is the y-intercept of \(f(x)\)?
3. How can you express \(f(x)\) in standard quadratic form?
4. What is the vertex of the parabola formed by \(f(x)\)?
5. How do you find the axis of symmetry for the function \(f(x)\)?

**Tip:** The Zero Product Property is a fundamental tool when dealing with factored polynomials.

Suppose f(x) = (x − 5)(x + 4). Solve (x − 5)(x + 4) = 0 for x.

Learn how to solve the quadratic equation (x − 5)(x + 4) = 0 using the Zero Product Property. This problem focuses on algebraic concepts like factoring and solving for roots. Suitable for students in Grades 8-10, with step-by-step instructions and related questions to deepen understanding.

Math Problem Statement

Suppose f ( x )

Solve ( x − 5 ) ( x + 4 )

Solution

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