Question

question
factor completely.
$3x^3 - 4x^2 + 12x - 16$

Explanation:

Step1: Group the terms

We group the first two terms and the last two terms together:
\((3x^{3}-4x^{2})+(12x - 16)\)

Step2: Factor out the GCF from each group

For the first group \(3x^{3}-4x^{2}\), the greatest common factor (GCF) is \(x^{2}\), so we factor it out: \(x^{2}(3x - 4)\)
For the second group \(12x-16\), the GCF is \(4\), so we factor it out: \(4(3x - 4)\)
Now the expression becomes: \(x^{2}(3x - 4)+4(3x - 4)\)

Step3: Factor out the common binomial factor

We can see that both terms have a common factor of \((3x - 4)\), so we factor that out:
\((3x - 4)(x^{2}+4)\)

Answer:

\((3x - 4)(x^{2}+4)\)