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

Question

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

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 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

Answer 1

To solve the quadratic equation \(7x^2 = 56x\) correctly, we need to follow these steps:

1. Put the quadratic in standard form: We rearrange the equation to \(7x^2 - 56x = 0\).
2. Factor out the GCF (Greatest Common Factor): The GCF here is \(7x\), so we factor it out to get \(7x(x - 8) = 0\).
3. Set each factor equal to zero: This gives us \(7x = 0\) and \(x - 8 = 0\).
4. Solve for \(x\):
   • From \(7x = 0\), we get \(x = 0\).
   • From \(x - 8 = 0\), we get \(x = 8\).

Therefore, the correct solutions are \(x = 0\) and \(x = 8\).

Now, reviewing the provided options, the correct sequence 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 \(x = 8\)

This matches with one of the responses you provided. The correct option 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 \(x = 8\).