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=−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=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=−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 should first put it into standard form:

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

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

3. **Set each factor equal to zero:**
\( 7x = 0 \) and \( x - 8 = 0 \)

4. **The solutions are:**
From \( 7x = 0 \), we get \( x = 0 \).
From \( x - 8 = 0 \), we get \( x = 8 \).

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

The response that correctly shows 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 \( x=8 \)"**