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

A. 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
B. 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

C. 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

B. 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
C. 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

D. 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 start by rearranging the equation into standard form:

  1. Put the quadratic in standard form: \[ 7x^2 - 56x = 0 \]

  2. Factor out the GCF (Greatest Common Factor): The 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: \[ x = 8 \]

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

The correct response that shows these steps is Option A and Option B (they are identical).

Therefore, both A and B are correct:

  • They both correctly detail the full process to put the equation in standard form, factor out the GCF, set the factors to zero, and find the appropriate solutions.

Responses C and D contain inaccuracies in the steps that do not lead to correct solutions to the equation.