1. The problem involves factoring the expression $12x^2 + 2x$. 2. To factor, we look for the greatest common factor (GCF) of the terms. 3. The terms are $12x^2$ and $2x$. The GCF of the coefficients 12 and 2 is 2. 4. Both terms have at least one $x$, so the GCF includes $x$. 5. Therefore, the GCF is $2x$. 6. Factor out $2x$ from each term: $$12x^2 + 2x = 2x(6x) + 2x(1) = 2x(6x + 1)$$ 7. The factored form is $2x(6x + 1)$. 8. This matches the visual representation where the top rectangle $12x^2 + 2x$ is split into two rectangles below: one labeled $I$ (likely representing the factor 1) and the other $2x$. Final answer: $$12x^2 + 2x = 2x(6x + 1)$$