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Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x^2=56x ?(1 point)

Responses

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
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 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=−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 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=−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

1 answer

Let's analyze the steps necessary to factor out the GCF and solve the quadratic equation \(7x^2 = 56x\).

  1. Put the quadratic in standard form: This involves rearranging the equation to set it to zero: \[ 7x^2 - 56x = 0 \]

  2. Factor out the GCF (Greatest Common Factor): The GCF of the terms \(7x^2\) and \(-56x\) is \(7x\). Factoring this out gives: \[ 7x(x - 8) = 0 \]

  3. Set each factor equal to zero: From \(7x(x - 8) = 0\), we set each factor to zero: \[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]

  4. Solve for \(x\): This gives: \[ x = 0 \quad \text{and} \quad x = 8 \]

The correct steps to factor out the GCF and solve the quadratic equation are:

  • 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 \(x = 8\)

Looking at the options provided, the correct response is the one that matches these steps closely. The responses that show the correct steps with the correct solutions are:

  • Response 1:

    • 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 \(x=8\)

  • Response 2:

    • Put the quadratic in standard form: \(7 x^2−56x=0\)
    • Factor out the GCF: \(7 x(x−8)=0\)
    • Set each factor equal to zero: \(7x=0\) and \(x−8=0\)
    • The solutions are: \(x=0\) and \(x=8\)

Both Response 1 and Response 2 are correct.