Question

A) Which of the following tables shows the correct steps to factor out the GCF and solve the
quadratic equation \(7x^2=56x\)? (1 point)
Put the quadratic in standard form \(7x^2-56x=0\)
Factor out the GCF \(7x\left(x-8\right)=0\)
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 \(7x^2-56x=0\)
Factor out the GCF \(7x\left(x-8\right)=0\)
Set each factor equal to zero \(7x=0\) and \(x-8=0\)
The solutions are \(x=0\) and \(x=8\)
Put the quadratic in standard form \(7x^2+56x=0\)
Factor out the GCF \(7x\left(x+8\right)=0\)
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 \(x-8=0\)
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 \(7x^2=56x\), let's go through the steps.

1. **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 \(7x\). Thus, we can factor it as:
\[
7x(x - 8) = 0
\]

3. **Set each factor equal to zero**:
Now we set each factor equal to zero:
- \(7x = 0\) which gives \(x = 0\)
- \(x - 8 = 0\) which gives \(x = 8\)

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

Now, let's evaluate the options provided:

1. **Option 1** states:
- Solutions are \(x = -7\) and \(x = 8\) – Incorrect.

2. **Option 2** states:
- Solutions are \(x = 0\) and \(x = 8\) – Correct.

3. **Option 3** states:
- Solutions are \(x = -8\) and \(x = 0\) – Incorrect.

4. **Option 4** states:
- Solutions are \(x = 8\) (no \(x=0\)) – Incorrect.

The correct choice that shows the proper steps to factor out the GCF and solve the quadratic equation \(7x^2 = 56x\) is the second option:
- **Put the quadratic in standard form \(7x^2 - 56x = 0\)**
- **Factor out the GCF \(7x\left(x-8\right)=0\)**
- **Set each factor equal to zero \(7x=0\) and \(x-8=0\)**
- **The solutions are \(x=0\) and \(x=8\)**.