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=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 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 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
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Answer 1

To solve the quadratic equation $7x^2=56x$, we first need to get it into standard form, which is $7x^2-56x=0$. Next, we factor out the greatest common factor (GCF), set each factor equal to zero, and then solve for $x$.

Let's go through the 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: $$7x=0\text{and}x-8=0$$

4. The solutions are: $$x=0\text{and}x=8$$

Based on this explanation, the correct option matches the steps laid out perfectly:

Put the quadratic in standard form $7x^2-56x=0$

Factor out the GCF $7x(x-8)=0$

Set each factor equal to zero $7x=0\text{ and }x-8=0$

The solutions are $x=0\text{ and }x=8$

Thus, the correct response is:

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