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
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
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Answer 1

Let's analyze the given quadratic equation and the responses provided to determine which shows the correct steps to factor out the GCF and solve the equation \(7x^2 = 56x\).

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

2. **Factor out the GCF:**
The greatest common factor (GCF) of \(7x^2\) and \(-56x\) is \(7x\). So we can 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 \(x\):**
- From \(7x = 0\), we get \(x = 0\).
- From \(x - 8 = 0\), we get \(x = 8\).

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

Now, we can check which response matches these steps accurately.

The correct response 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 \(x = 8\)

The two responses that match these steps are:
1. **Put the quadratic in standard form** \(7 x^2 - 56 x = 0\)
**Factor out the GCF** \(7 x \left( x - 8 \right) = 0\)
**Set each factor equal to zero** \(7x = 0\) and \(x - 8 = 0\)
**The solutions are** \(x = 0\) and \(x = 8\)

2. **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 \(x=8\)

Both are correct, providing the correct steps to factor out the GCF and solve the quadratic equation \(7x^2=56x\).