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=−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 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=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

Answer 1

To solve the quadratic equation \(7x^2 = 56x\), we first need to move all the terms to one side to put it in standard form:

1. Rearranging gives:
\[ 7x^2 - 56x = 0 \]

2. Next, we factor out the greatest common factor (GCF) which is \(7x\):
\[ 7x(x - 8) = 0 \]

3. Then, we set each factor equal to zero:
\[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]

4. Solving these equations gives:
- From \(7x = 0\), we get \(x = 0\)
- From \(x - 8 = 0\), we get \(x = 8\)

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

The correct response from the provided options 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 corresponds to the third option in your list.