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 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=−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=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=−8
and x=0
?(1 point)
Responses
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=−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=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=−8
and x=0
Answers
GPT-4o mini
To factor out the GCF and solve the quadratic equation \(7x^2 = 56x\), we can follow these correct steps:
1. **Put the quadratic in standard form**: Start by moving all terms to one side to set the equation to zero:
\[
7x^2 - 56x = 0
\]
2. **Factor out the GCF**: The greatest common factor (GCF) of the terms \(7x^2\) and \(-56x\) is \(7x\):
\[
7x(x - 8) = 0
\]
3. **Set each factor equal to zero**:
- \(7x = 0\)
- \(x - 8 = 0\)
4. **Solve for \(x\)**:
- From \(7x = 0\), we get \(x = 0\).
- From \(x - 8 = 0\), we get \(x = 8\).
Thus, the solutions are:
\[
x = 0 \quad \text{and} \quad x = 8
\]
The correct response from the options provided 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 the following option:
"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"
1. **Put the quadratic in standard form**: Start by moving all terms to one side to set the equation to zero:
\[
7x^2 - 56x = 0
\]
2. **Factor out the GCF**: The greatest common factor (GCF) of the terms \(7x^2\) and \(-56x\) is \(7x\):
\[
7x(x - 8) = 0
\]
3. **Set each factor equal to zero**:
- \(7x = 0\)
- \(x - 8 = 0\)
4. **Solve for \(x\)**:
- From \(7x = 0\), we get \(x = 0\).
- From \(x - 8 = 0\), we get \(x = 8\).
Thus, the solutions are:
\[
x = 0 \quad \text{and} \quad x = 8
\]
The correct response from the options provided 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 the following option:
"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"