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*Algebra 1 Practice - Solving a Quadratic Equation Using the Zero Product Property:*

The *Zero Product Property* states that if the product of two factors is zero, then at least one of the factors must be zero. This property is often used when a quadratic equation is factored into two binomials. Here's how to solve quadratic equations using the Zero Product Property.

Example Problem:
Solve the quadratic equation:
\[
(x - 3)(x + 5) = 0
\]

Steps:

1. **Set each factor equal to zero**:
According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor in the equation equal to zero:
\[
x - 3 = 0 \quad \text{or} \quad x + 5 = 0
\]

2. **Solve each equation**:
Now solve for \(x\) in each equation:
From \(x - 3 = 0\), add 3 to both sides:
\[
x = 3
\]
From \(x + 5 = 0\), subtract 5 from both sides:
\[
x = -5
\]

3. **Write the final solutions**:
The solutions to the equation \((x - 3)(x + 5) = 0\) are:
\[
x = 3 \quad \text{or} \quad x = -5
\]

Final Answer:
The solutions to the equation \((x - 3)(x + 5) = 0\) are \(x = 3\) and \(x = -5\).

Key Points to Remember:
**Zero Product Property**: If the product of two factors equals zero, then one or both factors must be zero.
**Factoring**: To use the Zero Product Property, the equation must first be factored into two binomials (or other factors).
**Solve each factor**: After setting each factor equal to zero, solve each resulting equation to find the values of \(x\).

This method is very useful for solving quadratic equations that are factorable, especially when the equation is already in factored form or can be easily factored.

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:

/ nickperich

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

#math #algebra #algebra2 #maths #math #shorts #funny #help #onlineclasses #onlinelearning #online #study