https://file.aiquickdraw.com/mathbot/file/1729772117186eftmbqan.jpg

Let's solve the three equations shown in the image:

### a. \((x - 4)(x - 5) = 0\)
We apply the zero product property, which states that if the product of two factors is 0, then at least one of the factors must be 0.

1. \(x - 4 = 0 \Rightarrow x = 4\)
2. \(x - 5 = 0 \Rightarrow x = 5\)

So, the solutions are **x = 4** and **x = 5**.

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### d. \((2x - 1)(x + 4) = 0\)
Again, applying the zero product property:

1. \(2x - 1 = 0 \Rightarrow 2x = 1 \Rightarrow x = \frac{1}{2}\)
2. \(x + 4 = 0 \Rightarrow x = -4\)

So, the solutions are **x = \(\frac{1}{2}\)** and **x = -4**.

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### g. \((x - 7)(x - 9) = 0\)
Using the zero product property one more time:

1. \(x - 7 = 0 \Rightarrow x = 7\)
2. \(x - 9 = 0 \Rightarrow x = 9\)

So, the solutions are **x = 7** and **x = 9**.

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Would you like further explanations on any of these? Here are five related questions:

1. How does the zero product property work?
2. What happens when one side of the equation is not zero?
3. How would you solve a quadratic equation if it was not factored?
4. Can you graph these solutions on a number line?
5. What is the relationship between factoring and solving quadratic equations?

**Tip:** Always check if the equation can be factored easily before using more advanced methods to solve quadratics.

(x - 4)(x - 5) = 0, (2x - 1)(x + 4) = 0, (x - 7)(x - 9) = 0

Learn how to solve quadratic equations by factoring and applying the zero product property. The example covers solving (x - 4)(x - 5) = 0, (2x - 1)(x + 4) = 0, and (x - 7)(x - 9) = 0. Suitable for students in Grades 8-10.

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