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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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1 answer

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 \(7x^2=56x\).