1. **State the problem:** Factorise the quadratic expression $6x^2 + 11x + 4$. 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, $a=6$, $b=11$, $c=4$. So, $a \times c = 6 \times 4 = 24$. 4. **Find two numbers that multiply to 24 and add to 11:** These numbers are 8 and 3 because $8 \times 3 = 24$ and $8 + 3 = 11$. 5. **Rewrite the middle term using these numbers:** $$6x^2 + 8x + 3x + 4$$ 6. **Group terms:** $$ (6x^2 + 8x) + (3x + 4) $$ 7. **Factor each group:** $$ 2x(3x + 4) + 1(3x + 4) $$ 8. **Factor out the common binomial:** $$ (3x + 4)(2x + 1) $$ **Final answer:** The factorised form of $6x^2 + 11x + 4$ is $$ (3x + 4)(2x + 1) $$.