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=−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=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 0 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=−8
and x=0

Answer 1

To solve the quadratic equation \(7x^2 = 56x\), we will first rearrange it into standard form, then factor it, and finally find the solutions. Here are the correct steps:

1. **Put the quadratic in standard form:**
Move all terms to one side:
\(7x^2 - 56x = 0\)

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

3. **Set each factor equal to zero:**
\(7x = 0\) and \(x - 8 = 0\)

4. **The solutions are:**
For \(7x = 0\), \(x = 0\)
For \(x - 8 = 0\), \(x = 8\)

Thus, the solutions to the quadratic equation are \(x = 0\) and \(x = 8\).

The correct response from the options provided 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 \(x = 8\)