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=−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=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=−7 and x=8

Answer 1

To solve the quadratic equation \(7x^2 = 56x\), you should first rearrange it into standard form, which is \(7x^2 - 56x = 0\).

Next, you factor out the greatest common factor (GCF), which is \(7x\). This gives us:

\[ 7x(x - 8) = 0. \]

Then, you set each factor equal to zero:

1. \(7x = 0\) leads to \(x = 0\).
2. \(x - 8 = 0\) leads to \(x = 8\).

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

The correct response based on these steps 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 \(x = 8\)

Please note that if any of the responses are repeated in a similar format with the same answer, they can also be considered correct.