(5-x)(2x+7)(x-3) =0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (5-x)(2x+7)(x-3) = 0

This equation represents a cubic polynomial set equal to zero. To solve for the values of x that satisfy this equation, we can use the Zero Product Property. This property states that if the product of several factors is equal to zero, then at least one of the factors must be zero.

Let's break down the equation:

• Factor 1: (5 - x)
• Factor 2: (2x + 7)
• Factor 3: (x - 3)

To find the solutions, we need to find the values of x that make each factor equal to zero.

Solving for x:

1. Factor 1: (5 - x) = 0

   • Add x to both sides: 5 = x
   • Therefore, x = 5 is one solution.

2. Factor 2: (2x + 7) = 0

   • Subtract 7 from both sides: 2x = -7
   • Divide both sides by 2: x = -7/2
   • Therefore, x = -7/2 is another solution.

3. Factor 3: (x - 3) = 0

   • Add 3 to both sides: x = 3
   • Therefore, x = 3 is the final solution.

Conclusion:

The solutions to the equation (5-x)(2x+7)(x-3) = 0 are x = 5, x = -7/2, and x = 3. These values represent the points on the x-axis where the graph of the cubic polynomial intersects the x-axis.