Quadratic equation by factoring 8x²-2x=0

To solve the quadratic equation \(8x^2 - 2x = 0\) by factoring, follow these steps:

1. **Set the equation to zero**: 
   \[
   8x^2 - 2x = 0
   \]

2. **Factor out the greatest common factor (GCF)**: 
   The GCF of \(8x^2\) and \(-2x\) is \(2x\). Factor \(2x\) out of the equation:
   \[
   2x(4x - 1) = 0
   \]

3. **Set each factor equal to zero**: 
   For the equation to be true, either \(2x = 0\) or \(4x - 1 = 0\).

   - For \(2x = 0\):
     \[
     x = 0
     \]

   - For \(4x - 1 = 0\):
     \[
     4x = 1 \implies x = \frac{1}{4}
     \]

4. **Combine the solutions**: 
   The solutions to the equation are:
   \[
   x = 0 \quad \text{and} \quad x = \frac{1}{4}
   \]

Thus, the solutions to the quadratic equation \(8x^2 - 2x = 0\) by factoring are \(x = 0\) and \(x = \frac{1}{4}\).

Would you like more details or have any questions about this process?

Here are 8 related questions to further your understanding:

1. How do you find the greatest common factor (GCF) of two terms?
2. Can every quadratic equation be solved by factoring?
3. What are other methods to solve quadratic equations besides factoring?
4. How do you check if the factored form of a quadratic equation is correct?
5. What is the quadratic formula and how is it used?
6. How does completing the square work for solving quadratic equations?
7. What are the key features of the graph of a quadratic function?
8. How do the solutions to a quadratic equation relate to its graph?

**Tip:** Always check your factored form by expanding it back to ensure it matches the original equation. This helps to verify your factoring is correct.

Learn how to solve the quadratic equation 8x² - 2x = 0 using the method of factoring. Follow a step-by-step explanation with examples. This problem covers key algebraic concepts, including quadratic equations, factoring, and the zero product property. Suitable for high school students.

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