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 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=−7 and x=8 Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals negative 7 and 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=8Put the quadratic in standard form 7 x squared minus 56 x equals 0 Factor out the GCF 7 x left parenthesis x minus 8 right parenthesis equals 0 Set each factor equal to zero 7 x equals 0 and x minus 8 equals 0 The solutions are x equals 0 and x equals 8

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=−8 and x=0

Answer 1

To solve the quadratic equation \(7x^2 = 56x\), we start by moving everything to one side to put it in standard form:

1. **Put the quadratic in standard form**:
\[
7x^2 - 56x = 0
\]

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

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

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

Thus, the correct steps are captured in the following response:

**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 \(x = 8\)

This matches the second option in your list:

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