Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x^2=56x

Question

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

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	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=−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

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

GPT-4o mini · Answer

To solve the quadratic equation $7x^2 = 56x$, we first need to rearrange it into standard form, factor it, and then find the solutions. Let's break down the correct steps: 1. **Put the quadratic in standard form**: $$ 7x^2 - 56x = 0 $$ 2. **Factor out the GCF**: $$ 7x(x - 8) = 0 $$ 3. **Set each factor equal to zero**: $$ 7x = 0 \quad \text{and} \quad x - 8 = 0 $$ 4. **The solutions are**: $$ x = 0 \quad \text{and} \quad x = 8 $$ Given these steps, the first response provided matches exactly: **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 the first option you listed.