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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 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

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

1 answer

The correct steps to factor out the GCF and solve the quadratic equation \( 7x^2 = 56x \) are as follows:

  1. Put the quadratic in standard form: Move all terms to one side to set the equation to zero: \[ 7x^2 - 56x = 0 \]

  2. Factor out the GCF: The greatest common factor (GCF) of the terms is \( 7x \): \[ 7x(x - 8) = 0 \]

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

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

Based on this breakdown, 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 \( x = 8 \)

So the correct table is the second option you provided.