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

Question

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=−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
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=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

Answer 1

To solve the quadratic equation $7x^2=56x$ correctly, we need to follow these steps:

1. Put the quadratic in standard form: We rearrange the equation to $7x^2-56x=0$.
2. Factor out the GCF (Greatest Common Factor): The GCF here is $7x$, so we factor it out to get $7x(x-8)=0$.
3. Set each factor equal to zero: This gives us $7x=0$ and $x-8=0$.
4. Solve for $x$:
   • From $7x=0$, we get $x=0$.
   • From $x-8=0$, we get $x=8$.

Therefore, the correct solutions are $x=0$ and $x=8$.

Now, reviewing the provided options, the correct sequence 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 $x=8$

This matches with one of the responses you provided. The correct option 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 $x=8$.