A) Which of the following tables shows the correct steps to factor out the GCF and solve the

Question

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 \(x=8\).