1. **State the problem:** Factor the quadratic expression $y = 8x^2 + 19x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $a \times c$ and add to $b$. 3. **Calculate the product and sum:** Here, $a = 8$, $b = 19$, and $c = 6$. So, $a \times c = 8 \times 6 = 48$. 4. **Find two numbers that multiply to 48 and add to 19:** These numbers are 16 and 3 because $16 \times 3 = 48$ and $16 + 3 = 19$. 5. **Rewrite the middle term using these numbers:** $$8x^2 + 16x + 3x + 6$$ 6. **Group terms:** $$ (8x^2 + 16x) + (3x + 6) $$ 7. **Factor each group:** $$ 8x(x + 2) + 3(x + 2) $$ 8. **Factor out the common binomial:** $$ (8x + 3)(x + 2) $$ **Final answer:** $$y = (8x + 3)(x + 2)$$