Question

1. $4x^4 - 12x^3 + 8x^2$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(4x^4\), \(-12x^3\), and \(8x^2\) is \(4x^2\). Factor it out:
\(4x^4 - 12x^3 + 8x^2 = 4x^2(x^2 - 3x + 2)\)

Step2: Factor the quadratic

Factor the quadratic \(x^2 - 3x + 2\). We need two numbers that multiply to \(2\) and add to \(-3\). Those numbers are \(-1\) and \(-2\):
\(x^2 - 3x + 2 = (x - 1)(x - 2)\)

Step3: Combine the factors

Putting it all together, the factored form is:
\(4x^2(x - 1)(x - 2)\)

Answer:

\(4x^2(x - 1)(x - 2)\)