Questions: Recognize the type of expression and use an appropriate method to factor it com x^3+14 x^2+49 x

Recognize the type of expression and use an appropriate method to factor it:
\[ x^{3}+14 x^{2}+49 x \]

Identify the common factor

The expression \(x^{3}+14 x^{2}+49 x\) has a common factor of \(x\) in all terms.

Factor out the common factor

Factor out \(x\) from the expression:
\[ x(x^{2} + 14x + 49) \]

Factor the quadratic expression

The quadratic expression \(x^{2} + 14x + 49\) is a perfect square trinomial. It can be factored as:
\[ (x + 7)^2 \]

Write the fully factored form

Combine the results to write the fully factored form of the original expression:
\[ x(x + 7)^2 \]

The factored form of the expression is \(\boxed{x(x + 7)^2}\).

The factored form of the expression is \(\boxed{x(x + 7)^2}\).