4x^3-20x^2-24x
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To simplify the expression 4x^3 - 20x^2 - 24x, we can factor out the greatest common factor (GCF) from all the terms.
Step 1: Find the GCF of all the terms.
In this case, the GCF of 4, 20, and 24 is 4, and the GCF of x^3, x^2, and x is x.
Step 2: Factor out the GCF from each term.
Factoring out 4x from each term gives us:
4x(x^2 - 5x - 6)
Step 3: Simplify the factored expression.
The expression inside the parentheses (x^2 - 5x - 6) can be further factored, by finding two numbers that multiply to -6 and add up to -5. In this case, the numbers are -6 and 1. So, we can rewrite the expression as:
4x(x - 6)(x + 1)
Therefore, the simplified form of the expression 4x^3 - 20x^2 - 24x is 4x(x - 6)(x + 1).