Question

1. $3x^3 - 3x^2 - 60x$

Explanation:

Step1: Factor out the greatest common factor (GCF)

The GCF of \(3x^3\), \(-3x^2\), and \(-60x\) is \(3x\). So we factor out \(3x\) from each term:
\(3x^3 - 3x^2 - 60x = 3x(x^2 - x - 20)\)

Step2: Factor the quadratic expression

Now we factor the quadratic \(x^2 - x - 20\). We need two numbers that multiply to \(-20\) and add up to \(-1\). The numbers are \(-5\) and \(4\) because \((-5)\times4=-20\) and \(-5 + 4=-1\). So we can factor \(x^2 - x - 20\) as \((x - 5)(x + 4)\).

Putting it all together, the fully factored form is:
\(3x(x - 5)(x + 4)\)

Answer:

\(3x(x - 5)(x + 4)\)