Factor Quadratic B6730E
Let's factor the expression $x^2 - 5x - 6$ step by step!
1. Imagine you have $x^2$, which is $x$ times $x$:
❌ ❌ (2 x's)
2. Now, we want to find two numbers that multiply to $-6$ and add to $-5$.
3. Think of pairs of numbers for $-6$:
2️⃣ 3️⃣, -2️⃣ -3️⃣, 6️⃣ 1️⃣, -6️⃣ -1️⃣
4. Which pair adds to $-5$? Let's check:
- $2 + 3 = 5$
- $-2 + (-3) = -5$ ✅
5. So, the numbers are $-2$ and $3$ (but we want the product to be $-6$ and sum $-5$, so actually $-6$ and $1$ or $1$ and $-6$? Wait, let's test $-6$ and $1$:
- $-6 + 1 = -5$ and $-6 imes 1 = -6$ ✅
6. Great! The numbers are $-6$ and $1$.
7. So, factor like this:
**Box 1:**
Group 1:
❌ ➕ 6️⃣
($x - 6$)
Add ➕
**Box 2:**
❌ ➕ 6️⃣
($x - 6$)
Group 2:
❌ ➕ 1️⃣
($x + 1$)
=
**Total box:**
❌ ➕ 1️⃣
($x + 1$)
❌ ❌ ➕ 6️⃣ 1️⃣
$(x - 6)(x + 1)$
And that's the factored form! 🎉$(x - 6)(x + 1)$