Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x?(1 point)

Responses

1 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

2 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=8Put 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

3 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

4 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

1 answer

To solve the quadratic equation \(7x^2 = 56x\), we will follow the correct steps to rewrite the equation, factor out the greatest common factor (GCF), set each factor to zero, and find the solutions.

  1. Put the quadratic in standard form: First, we need to rewrite the equation as follows: \[ 7x^2 - 56x = 0 \]

  2. Factor out the GCF: The GCF of the terms \(7x^2\) and \(-56x\) is \(7x\), so we factor it out: \[ 7x(x - 8) = 0 \]

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

    • From \(7x = 0\), we get \(x = 0\).
    • From \(x - 8 = 0\), we get \(x = 8\).
  4. The solutions are: \[ x = 0 \quad \text{and} \quad x = 8 \]

Now, let's compare this with the provided options:

  • Option 1 is incorrect.
  • Option 2 is correct: The steps are accurately described, leading to the correct solutions of \(x = 0\) and \(x = 8\).
  • Option 3 is incorrect: It states that one solution is \(x = -7\), which is wrong.
  • Option 4 is incorrect: The equation is incorrectly written as \(7x^2 + 56x = 0\), and it has incorrect solutions.

Thus, the correct response is Option 2.