Question

Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x^2=56x
?(1 point)
Responses

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
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 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=−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 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=−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 factor out the GCF and solve the quadratic equation \( 7x^2 = 56x \), we follow these steps:

1. **Put the quadratic in standard form**: Subtract \( 56x \) from both sides to get \( 7x^2 - 56x = 0 \).

2. **Factor out the GCF**: The GCF of \( 7x^2 \) and \( 56x \) is \( 7x \). Factoring gives us \( 7x(x - 8) = 0 \).

3. **Set each factor equal to zero**:
- From \( 7x = 0 \), we get \( x = 0 \).
- From \( x - 8 = 0 \), we get \( x = 8 \).

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

Now, let's analyze the responses:

1. **Response 1**: This matches all the correct steps and gives the correct solutions \( x = 0 \) and \( x = 8 \).

2. **Response 2**: This also matches the correct steps and gives the correct solutions \( x = 0 \) and \( x = 8 \).

3. **Response 3**: Incorrect solutions of \( x = -7 \) instead of \( x = 0 \).

4. **Response 4**: Incorrectly uses \( 7x^2 + 56x = 0 \); it should be \( 7x^2 - 56x = 0 \).

5. **Response 5**: Incorrectly states \( x-8 = 0 \) without setting the equation correctly from standard form.

Therefore, the first and the second responses are correct:

- **Correct Response**: Response 1 and Response 2 both accurately describe the steps to factor out the GCF and solve the quadratic equation.