Question

Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x^2 = 56x

Answer 1

To factor out the greatest common factor (GCF) and solve the quadratic equation \( 7x^2 = 56x \), we can follow these steps:

1. **Set the equation to zero**: First, we want to bring all terms to one side of the equation to set it to zero:
\[
7x^2 - 56x = 0
\]

2. **Find the GCF**: The GCF of the terms \( 7x^2 \) and \( -56x \) is \( 7x \).

3. **Factor out the GCF**:
\[
7x(x - 8) = 0
\]

4. **Set each factor to zero**: According to the zero product property, if the product is zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero:
\[
7x = 0 \quad \text{or} \quad x - 8 = 0
\]

5. **Solve each equation**:
- From \( 7x = 0 \):
\[
x = 0
\]
- From \( x - 8 = 0 \):
\[
x = 8
\]

6. **Final solutions**: The solutions to the equation are:
\[
x = 0 \quad \text{or} \quad x = 8
\]

In summary, the steps to factor and solve the equation \( 7x^2 = 56x \) are:
- Set equation to zero: \( 7x^2 - 56x = 0 \)
- Factor out the GCF: \( 7x(x - 8) = 0 \)
- Solve for \( x \): \( x = 0 \) or \( x = 8 \)

If you have the specific tables you would like to compare, please provide them, and I can help you determine which one shows these steps correctly.