Today we will solve the quadratic equation x squared plus 5x plus 6 equals 0 using the factoring method. We need to find two numbers that multiply to 6 and add to 5.
Let's find the factor pairs of 6. The pairs are 1 times 6 which sum to 7, and 2 times 3 which sum to 5. Since we need factors that sum to 5, we use 2 and 3. This gives us the factored form: x plus 2 times x plus 3 equals 0.
Now we apply the zero product property. This property states that if A times B equals zero, then either A equals zero or B equals zero. Applying this to our factored equation, we get x plus 2 equals zero or x plus 3 equals zero.
Now we solve each equation separately. From x plus 2 equals zero, we subtract 2 from both sides to get x equals negative 2. From x plus 3 equals zero, we subtract 3 from both sides to get x equals negative 3.
To summarize our solution: We started with x squared plus 5x plus 6 equals 0. We factored it into x plus 2 times x plus 3 equals 0. Using the zero product property, we found that x equals negative 2 and x equals negative 3 are the solutions.