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Factor the expression completely 10x^2 + 5x

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To factor the expression \(10x^2 + 5x\) completely, we can start by identifying the greatest common factor (GCF) of the terms.

  1. The GCF of the coefficients \(10\) and \(5\) is \(5\).
  2. Both terms also contain the variable \(x\), so we can factor out \(5x\).

Now we factor \(5x\) out of each term:

\[ 10x^2 + 5x = 5x(2x + 1) \]

The expression \(10x^2 + 5x\) is completely factored as:

\[ \boxed{5x(2x + 1)} \]