Question

Factorie completely 3x^3-x^2-12x+4

Answer 1

To factor the polynomial \( 3x^3 - x^2 - 12x + 4 \), we can start by rearranging it in standard form:

\[
3x^3 - x^2 - 12x + 4
\]

Next, we can use the method of grouping. We'll group the terms in pairs:

\[
(3x^3 - x^2) + (-12x + 4)
\]

Now factor out the common factors from each group:

\[
x^2(3x - 1) - 4(3x - 1)
\]

Notice that \( (3x - 1) \) is a common factor. We can factor that out:

\[
(3x - 1)(x^2 - 4)
\]

Now, we recognize that \( x^2 - 4 \) is a difference of squares, which can be factored further:

\[
x^2 - 4 = (x - 2)(x + 2)
\]

Putting it all together, we have:

\[
3x^3 - x^2 - 12x + 4 = (3x - 1)(x - 2)(x + 2)
\]

Thus, the complete factorization of the polynomial \( 3x^3 - x^2 - 12x + 4 \) is:

\[
\boxed{(3x - 1)(x - 2)(x + 2)}
\]