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=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=−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=−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

Answer 1

To solve the quadratic equation \(7x^2 = 56x\), we first need to transform it into standard form by moving all terms to one side.

1. **Put the quadratic in standard form:**
\[
7x^2 - 56x = 0
\]

2. **Factor out the GCF:**
The greatest common factor (GCF) is \(7x\).
\[
7x(x - 8) = 0
\]

3. **Set each factor equal to zero:**
\[
7x = 0 \quad \text{and} \quad x - 8 = 0
\]

4. **Solve for \(x\):**
- From \(7x = 0\), we get \(x = 0\).
- From \(x - 8 = 0\), we get \(x = 8\).

Thus, the solutions are:
\[
x = 0 \quad \text{and} \quad x = 8
\]

The correct response includes:

- Putting the quadratic in standard form as \(7x^2 - 56x = 0\),
- Factoring out the GCF to get \(7x(x - 8) = 0\),
- Setting each factor equal to zero,
- Concluding the solutions are \(x = 0\) and \(x = 8\).

The choice that matches this description is the second option:

**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 \(x = 8\)