Question: Factor the trinomial: 5x squared plus 29x plus 20
1. **State the problem:** Factor the trinomial $$5x^2 + 29x + 20$$.
2. **Recall the factoring method for trinomials:** For a quadratic in the form $$ax^2 + bx + c$$, we look for two numbers that multiply to $$a \times c$$ and add to $$b$$.
3. **Calculate the product $$a \times c$$:** Here, $$a = 5$$ and $$c = 20$$, so $$5 \times 20 = 100$$.
4. **Find two numbers that multiply to 100 and add to 29:** These numbers are $$25$$ and $$4$$ because $$25 \times 4 = 100$$ and $$25 + 4 = 29$$.
5. **Rewrite the middle term using these numbers:**
$$5x^2 + 25x + 4x + 20$$
6. **Group terms:**
$$(5x^2 + 25x) + (4x + 20)$$
7. **Factor each group:**
$$5x(x + 5) + 4(x + 5)$$
8. **Factor out the common binomial:**
$$(5x + 4)(x + 5)$$
**Final answer:** $$\boxed{(5x + 4)(x + 5)}$$