Factorise Quadratic C4841F

1. **State the problem:** We need to fully factorise the quadratic expression $$3t^2 + 16t + 5$$. 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 product and sum:** Here, $$a = 3$$, $$b = 16$$, and $$c = 5$$. Calculate product: $$3 \times 5 = 15$$. We need two numbers that multiply to $$15$$ and add to $$16$$. 4. **Find the numbers:** The numbers are $$15$$ and $$1$$ because $$15 \times 1 = 15$$ and $$15 + 1 = 16$$. 5. **Rewrite the middle term:** Rewrite $$16t$$ as $$15t + 1t$$: $$3t^2 + 15t + 1t + 5$$ 6. **Group terms:** Group the first two and last two terms: $$(3t^2 + 15t) + (1t + 5)$$ 7. **Factor each group:** $$3t(t + 5) + 1(t + 5)$$ 8. **Factor out the common binomial:** $$(3t + 1)(t + 5)$$ 9. **Final answer:** The fully factorised form is $$\boxed{(3t + 1)(t + 5)}$$.