Question

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 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
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 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

Answer 1

To factor the quadratic equation \( 7x^2 = 56x \), we first need to put it in standard form and find the correct steps.

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

2. **Factor out the GCF (Greatest Common Factor):**
The GCF here is \( 7x \), so we factor it out:
\[
7x(x - 8) = 0
\]

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

4. **Solve for \( x \):**
For \( 7x = 0 \):
\[
x = 0
\]
For \( x - 8 = 0 \):
\[
x = 8
\]

5. **The solutions are:**
\[
x = 0 \quad \text{and} \quad x = 8
\]

Based on these steps, the correct table of solutions 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 \( x = 8 \)

So, the correct response from your options is:
"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."