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Answer
1. \( m^{2} - 9m + 20 = (m - 4)(m - 5) \)
2. \( a^{2} + 10a + 24 = (a + 4)(a + 6) \)
Solution
1. Para \( m^{2} - 9m + 20 \):
- Buscamos dos números que al multiplicarlos den \(20\) y al sumarlos den \(-9\).
- Los números \(-4\) y \(-5\) cumplen:
- Producto: \((-4)(-5) = 20\).
- Suma: \(-4 + (-5) = -9\).
- Por lo tanto, se puede factorizar como:
\[
m^{2} - 9m + 20 = (m - 4)(m - 5)
\]
2. Para \( a^{2} + 10a + 24 \):
- Buscamos dos números que al multiplicarse den \(24\) y al sumarse den \(10\).
- Los números \(4\) y \(6\) cumplen:
- Producto: \(4 \times 6 = 24\).
- Suma: \(4 + 6 = 10\).
- Así, la factorización es:
\[
a^{2} + 10a + 24 = (a + 4)(a + 6)
\]
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Simplify this solution The Deep Dive
To add a little excitement, let's dive into some fun facts about solving quadratic equations! For \( m^{2}-9m+20=0 \), you can factor it as \( (m-4)(m-5)=0 \). This means \( m \) could be either 4 or 5. Finding roots can sometimes feel like a treasure hunt—who doesn't love uncovering hidden gems? Now for \( a^{2}+10a+24=0 \), you can factor this one too as \( (a+6)(a+4)=0 \). Solving results in \( a = -6 \) or \( a = -4 \). It's like solving a mystery; each root leads you deeper into the world of math adventures!
