9.

Factor the expression.

3x3 + 3x2 + x + 1

x(3x2 + x + 1)

3x2(x + 1)

(x + 3)(3x2 – 1)

(x + 1)(3x2 + 1)

1 answer

To factor the given expression \(3x^3 + 3x^2 + x + 1\), let's follow systematic steps of factoring:

1. **Group Terms**: Group the terms in pairs.
\[
(3x^3 + 3x^2) + (x + 1)
\]

2. **Factor Out Common Terms in Each Group**:
\[
3x^2(x + 1) + 1(x + 1)
\]

3. **Factor Out the Common Binomial Factor**:
\[
(x + 1)(3x^2 + 1)
\]

So the factored form of the expression \( 3x^3 + 3x^2 + x + 1 \) is \((x + 1)(3x^2 + 1)\).

Hence, the correct option is:
\[
(x + 1)(3x^2 + 1)
\]