(x+1)(3x+4)=0 Zero Product Property

Jasonbradley

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Jun 16, 2024

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Solving Equations Using the Zero Product Property

The Zero Product Property is a fundamental concept in algebra that states: If the product of two or more factors is zero, then at least one of the factors must be zero.

This property is extremely useful for solving equations where one side is a product of factors and the other side is zero. Let's see how it works with the equation:

(x + 1)(3x + 4) = 0

1. Identify the Factors:

We have two factors in this equation:

• (x + 1)
• (3x + 4)

2. Apply the Zero Product Property:

According to the property, for the product of these factors to be zero, at least one of them must be equal to zero. Therefore, we have two possible cases:

• Case 1: (x + 1) = 0
• Case 2: (3x + 4) = 0

3. Solve for x in each case:

• Case 1:

  • Subtract 1 from both sides: x = -1

• Case 2:

  • Subtract 4 from both sides: 3x = -4
  • Divide both sides by 3: x = -4/3

4. Solutions:

We have found two solutions for the equation:

• x = -1
• x = -4/3

Conclusion:

Using the Zero Product Property, we were able to solve the equation (x + 1)(3x + 4) = 0 by setting each factor equal to zero and solving for x. This property is a powerful tool for solving equations in algebra, and it's essential to understand how it works.