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To factor the polynomial \( x^3 - 6x^2 - 5x \), you can follow these steps: 1. **Factor out the greatest common factor (GCF):** The GCF of \( x^3, -6x^2, \) and \( -5x \) is \( x \). So, factor \( x \) out: \[ x^3 - 6x^2 - 5x = x(x^2 - 6x - 5) \] 2. **Factor the quadratic expression \( x^2 - 6x - 5 \):** To factor the quadratic \( x^2 - 6x - 5 \), look for two numbers that multiply to \(-5\) and add to \(-6\): - The numbers \(-1\) and \(-5\) work because: \[ -1 \cdot 5 = -5 \quad \text{and} \quad -1 + 5 = -6 \] So, we can write the quadratic as: \[ x^2 - 6x - 5 = (x - 1)(x - 5) \] 3. **Combine the factored terms:** Substitute the factored quadratic back into the expression: \[ x(x^2 - 6x - 5) = x(x - 1)(x - 5) \] So, the completely factored form of \( x^3 - 6x^2 - 5x \) is: \[ \boxed{x(x - 1)(x - 5)} \]

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