Question

factor the polynomial.
4n^3-12n^2+3n-9

Answer 1

To factor the polynomial \( 4n^3 - 12n^2 + 3n - 9 \), we can begin by grouping the terms.

First, we can group the first two terms and the last two terms:

\[
(4n^3 - 12n^2) + (3n - 9)
\]

Now, we can factor out the greatest common factor from each group:

1. For \( 4n^3 - 12n^2 \), the GCF is \( 4n^2 \):
\[
4n^2(n - 3)
\]

2. For \( 3n - 9 \), the GCF is \( 3 \):
\[
3(n - 3)
\]

Now, substitute these factored forms back into the expression:

\[
4n^2(n - 3) + 3(n - 3)
\]

Notice that \( (n - 3) \) is a common factor:

\[
(n - 3)(4n^2 + 3)
\]

Thus, the factored form of the polynomial \( 4n^3 - 12n^2 + 3n - 9 \) is:

\[
(n - 3)(4n^2 + 3)
\]