Question

25-26 pre-college math semester a exam (part 2)
question 3
completely factor each expression:
d. $3x^3 - 12x$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(3x^3\) and \(-12x\) is \(3x\). Factor it out:
\(3x^3 - 12x = 3x(x^2 - 4)\)

Step2: Factor the difference of squares

The expression \(x^2 - 4\) is a difference of squares, which can be factored as \((x - 2)(x + 2)\) (since \(a^2 - b^2=(a - b)(a + b)\) with \(a = x\) and \(b = 2\)).
So, substitute back:
\(3x(x^2 - 4)=3x(x - 2)(x + 2)\)

Answer:

\(3x(x - 2)(x + 2)\)