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

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**:
\[
7x = 0 \quad \text{and} \quad x - 8 = 0
\]

4. **The solutions are**:
\[
x = 0 \quad \text{and} \quad x = 8
\]

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**