Ask a New Question
Menu

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=−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

1 answer

To factor out the GCF and solve the quadratic equation \(7x^2 = 56x\), we can follow these correct steps:

  1. Put the quadratic in standard form: Start by moving 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 \(7x^2\) and \(-56x\) is \(7x\): \[ 7x(x - 8) = 0 \]

  3. Set each factor equal to zero:

    • \(7x = 0\)
    • \(x - 8 = 0\)

  4. Solve for \(x\):

    • From \(7x = 0\), we get \(x = 0\).
    • From \(x - 8 = 0\), we get \(x = 8\).

Thus, the solutions are: \[ x = 0 \quad \text{and} \quad x = 8 \]

The correct response from the options provided 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 \(x = 8\)

This matches the following option: "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"