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=−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

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 \( 7x^2 = 56x \), we first move all terms 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: \[ x = 0 \quad \text{and} \quad x = 8 \]

Therefore, the correct response is the one that states the steps to solve the equation correctly as follows:

• 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 \( x = 8 \)

The correct responses are:

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: \( 7x = 0 \) and \( x - 8 = 0 \)
4. The solutions are: \( x = 0 \) and \( x = 8 \)