`f(x)=x^(3)+5x^(2)-4x-20`
How many of the zeros of funtion f defined by the equation above are located in the interval `-4lexle4`?

Answer

To find how many zeros of the function \( f(x) = x^3 + 5x^2 - 4x - 20 \) are located in the interval \([-4, 4]\), we will evaluate the function at various integer points within this interval and check for roots.

### Step-by-Step Solution:

1. **Identify the function and the interval**:
\[ f(x) = x^3 + 5x^2 - 4x - 20 \]
We are interested in the interval \([-4, 4]\).

2. **Determine the factors of the constant term**:
The constant term of the polynomial is \(-20\). The factors of \(-20\) that we will consider within the interval are:
\[ \pm 1, \pm 2, \pm 4 \]

3. **Evaluate the function at each integer in the interval**:
- **For \( x = -4 \)**:
\[ f(-4) = (-4)^3 + 5(-4)^2 - 4(-4) - 20 = -64 + 80 + 16 - 20 = 12 \quad (\text{not a zero}) \]
- **For \( x = -3 \)**:
\[ f(-3) = (-3)^3 + 5(-3)^2 - 4(-3) - 20 = -27 + 45 + 12 - 20 = 10 \quad (\text{not a zero}) \]
- **For \( x = -2 \)**:
\[ f(-2) = (-2)^3 + 5(-2)^2 - 4(-2) - 20 = -8 + 20 + 8 - 20 = 0 \quad (\text{zero found}) \]
- **For \( x = -1 \)**:
\[ f(-1) = (-1)^3 + 5(-1)^2 - 4(-1) - 20 = -1 + 5 + 4 - 20 = -12 \quad (\text{not a zero}) \]
- **For \( x = 0 \)**:
\[ f(0) = 0^3 + 5(0)^2 - 4(0) - 20 = -20 \quad (\text{not a zero}) \]
- **For \( x = 1 \)**:
\[ f(1) = 1^3 + 5(1)^2 - 4(1) - 20 = 1 + 5 - 4 - 20 = -18 \quad (\text{not a zero}) \]
- **For \( x = 2 \)**:
\[ f(2) = 2^3 + 5(2)^2 - 4(2) - 20 = 8 + 20 - 8 - 20 = 0 \quad (\text{zero found}) \]
- **For \( x = 3 \)**:
\[ f(3) = 3^3 + 5(3)^2 - 4(3) - 20 = 27 + 45 - 12 - 20 = 40 \quad (\text{not a zero}) \]
- **For \( x = 4 \)**:
\[ f(4) = 4^3 + 5(4)^2 - 4(4) - 20 = 64 + 80 - 16 - 20 = 108 \quad (\text{not a zero}) \]

4. **Count the zeros found**:
The zeros found in the interval \([-4, 4]\) are:
- \( x = -2 \)
- \( x = 2 \)

Thus, there are **2 zeros** of the function \( f(x) \) in the interval \([-4, 4]\).

### Final Answer:
The number of zeros of the function \( f(x) \) in the interval \([-4, 4]\) is **2**.