Answer
$(3 x - 1)(x^2+4)$
Work Step by Step
To factorize the given polynomial, we need to take some term that is a common factor and factor it out. We have:
$3 \cdot x^3 - x^2 + 12 \cdot x - 4$
We can write this polynomial as:
$ 3 \cdot x \cdot x^2 - 1 \cdot x^2 + 4 \cdot 3 \cdot x - 1 \cdot 4$
Now, we group terms and factor $x^2$ out from the first two terms. So:
$x^2 \cdot (3 \cdot x - 1) + 4 \cdot 3 \cdot x - 1 \cdot 4$
Now, we factor $4$ out from the last two terms:
$x^2 \cdot (3 \cdot x - 1) + 4 \cdot ( 3 \cdot x - 1) $
So, we can put the common factor, that is, 3 \cdot x - 1 in evidence, in order to get:
$(3x - 1) (x^2+4)$
