Question

Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x ?(1 point)
Responses

Put the quadratic in standard form x−8=0
Factor out the GCF No GCF
Set each factor equal to zero x−8=0
The solutions are x=8
Put the quadratic in standard form x minus 8 equals 0 Factor out the GCF No GCF Set each factor equal to zero x minus 8 equals 0 The solutions are x equals 8

Put the quadratic in standard form 7x2−56x=0
Factor out the GCF 7x(x−8)=0
Set each factor equal to zero 7x=0 and x−8=0
The solutions are x=0 and x=8

Answer 1

The correct steps to factor out the GCF and solve the quadratic equation \( 7x^2 = 56x \) are as follows:

1. **Put the quadratic in standard form**: Move all terms to one side to set the equation to zero:
\[
7x^2 - 56x = 0
\]

2. **Factor out the GCF**: The greatest common factor (GCF) of the terms is \( 7x \):
\[
7x(x - 8) = 0
\]

3. **Set each factor equal to zero**:
\[
7x = 0 \quad \text{and} \quad x - 8 = 0
\]

4. **The solutions are**:
\[
x = 0 \quad \text{and} \quad x = 8
\]

Based on this breakdown, the correct response is:

**Put the quadratic in standard form**: \( 7x^2 - 56x = 0 \)
**Factor out the GCF**: \( 7x(x - 8) = 0 \)
**Set each factor equal to zero**: \( 7x = 0 \) and \( x - 8 = 0 \)
**The solutions are**: \( x = 0 \) and \( x = 8 \)

So the correct table is the second option you provided.