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 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 \( x = 8 \)