1. **State the problem:** Factorize the quadratic expression $3x^2 + 10x + 8$. 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, $a = 3$, $b = 10$, and $c = 8$. So, $a \times c = 3 \times 8 = 24$. 4. **Find two numbers that multiply to 24 and add to 10:** These numbers are 6 and 4. 5. **Rewrite the middle term using these numbers:** $$3x^2 + 6x + 4x + 8$$ 6. **Group terms:** $$ (3x^2 + 6x) + (4x + 8) $$ 7. **Factor each group:** $$ 3x(x + 2) + 4(x + 2) $$ 8. **Factor out the common binomial:** $$ (3x + 4)(x + 2) $$ **Final answer:** The factorization of $3x^2 + 10x + 8$ is $$ (3x + 4)(x + 2) $$.