The expression 2x^3 + 4x^2 + x can be factored by first identifying the common factors in each term. In this case, we see that each term has a factor of x, and we can also factor out 2 from the first two terms. Here’s how to approach it step-by-step:
- Identify the common factors: Each term contains a factor of x.
- Factor out x: This simplifies the expression to x(2x^2 + 4x + 1).
- Next, we can observe the quadratic expression 2x^2 + 4x + 1.
- Now, we apply the quadratic formula or factoring methods to see if we can factor 2x^2 + 4x + 1 further. However, this particular quadratic does not factor easily into integers.
- Thus, the completely factored form of the original expression is x(2x^2 + 4x + 1).
In summary, the factored form of 2x^3 + 4x^2 + x is x(2x^2 + 4x + 1).