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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

A) 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

B) 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

C) 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

D) 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

1 answer

To solve the quadratic equation \(7x^2 = 56x\) by factoring out the greatest common factor (GCF), let's follow these steps:

  1. Put the quadratic in standard form: Rearranging the equation gives \(7x^2 - 56x = 0\).
  2. Factor out the GCF: The GCF of the terms is \(7x\), leading to \(7x(x - 8) = 0\).
  3. Set each factor equal to zero:
    • From \(7x = 0\), we find \(x = 0\).
    • From \(x - 8 = 0\), we find \(x = 8\).
  4. The solutions are: \(x = 0\) and \(x = 8\).

Now, let's evaluate the options provided:

Option A:

  • Correctly states the steps and solutions.
  • Solutions: \(x = 0\) and \(x = 8\).

Option B:

  • Incorrectly gives the solution as \(x = -7\).
  • Solutions: \(x = -7\) and \(x = 8\) (wrong).

Option C:

  • Incorrectly sets up the equation as \(7x^2 + 56x = 0\) (it should be negative).
  • Solutions: \(x = -8\) and \(x = 0\) (wrong).

Option D:

  • Does not approach the problem correctly since it skips factoring and jumps to a linear equation.
  • Solution: \(x = 8\) (incomplete and incorrect).

Based on the analysis, Option A is the correct choice as it effectively outlines the appropriate steps to factor and solve the quadratic equation \(7x^2 = 56x\).