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

Question

?(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=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
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 x−8=0
Factor out the GCF No GCF
Set each factor equal to zero x−8=0
The solutions are x=8

Answer 1

To solve the quadratic equation \( 7x^2 = 56x \), we first need to move everything to one side of the equation and set it to zero.

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: \[ x = 0 \quad \text{and} \quad x = 8 \]

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 \( x = 8 \)

Thus, the option that reflects this sequence accurately 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 \( x = 8 \)