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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=8Put 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=−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=−8 and x=0

1 answer

To solve the quadratic equation \( 7x^2 = 56x \), we first need to rewrite it in standard form, factor it, and then find the solutions. Let's go through the options.

  1. Put the quadratic in standard form:

    • Start by moving all terms to one side: \( 7x^2 - 56x = 0 \).

  2. Factor out the GCF (Greatest Common Factor):

    • The GCF of \( 7x^2 \) and \( -56x \) is \( 7x \).
    • Factoring it out gives: \( 7x(x - 8) = 0 \).

  3. Set each factor equal to zero:

    • Setting \( 7x = 0 \) gives \( x = 0 \).
    • Setting \( x - 8 = 0 \) gives \( x = 8 \).

  4. The solutions are:

    • The solutions are \( x = 0 \) and \( x = 8 \).

From the options listed, the second option correctly follows these steps:

  • 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 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 \( x=8 \)