Factor Out Common Terms in 4x²+2x: Algebraic Simplification

To factor the expression $4x^2 + 2x$, first notice that each term shares a common factor of $2x$: $\blue 2\cdot2\cdot \orange x\cdot x+\blue 2\cdot \orange x$

Start by factoring out $2x$:

$4x^2 + 2x = 2x(2x + 1)$

Thus, the factored expression is $2x(2x + 1)$, as $2 \cdot x$ is the common factor.