Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x ?(1 point)

Question

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=−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

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=−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

C .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
D .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	x−8=0
Factor out the GCF	No GCF
Set each factor equal to zero	x−8=0
The solutions are	x=8

GPT-4o mini · Answer

To solve the quadratic equation $ 7x^2 = 56x $, we first need to rearrange it into standard form: 1. Move all terms to one side: $$ 7x^2 - 56x = 0 $$ 2. Next, factor out the greatest common factor (GCF), which is $ 7x $: $$ 7x(x - 8) = 0 $$ 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 $. Thus, the solutions are $ x = 0 $ and $ x = 8 $. Looking at the provided options: - **Option incorrectly states the solutions as $ x = -7 $ and $ x = 8 $. - **Option B** incorrectly begins with $ 7x^2 + 56x = 0 $ and gives incorrect solutions $ x = -8 $ and $ x = 0 $. - **Option C** correctly puts the quadratic in standard form, factors it accurately, and gives mistaken solutions $ x = 0 $ and $ x = 8 $ (the correct solutions are fine, but the format is less informative). - **Option D** correctly describes the steps and keeps the notation clear, providing the correct solutions $ x = 0 $ and $ x = 8 $. - The last option incorrectly states that there is no GCF. The correct answer, in terms of clarity and accuracy with all steps shown, is **Option D**.