Question
Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x to the second power =56x
?(1 point)
Responses
A
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
B
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
C
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
D
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
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?(1 point)
Responses
A
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
B
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
C
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
D
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
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the quadratic equation \(7x^2 = 56x\) by factoring out the greatest common factor (GCF), we follow these steps:
1. **Put the quadratic in standard form**: First, we need to move all terms to one side of the equation:
\[
7x^2 - 56x = 0
\]
2. **Factor out the GCF**: The GCF of \(7x^2\) and \(-56x\) is \(7x\):
\[
7x(x - 8) = 0
\]
3. **Set each factor equal to zero**:
- From \(7x = 0\), we find \(x = 0\).
- From \(x - 8 = 0\), we find \(x = 8\).
Therefore, the solutions to the equation are \(x = 0\) and \(x = 8\).
Now let's analyze the response options:
- **Option A**: This option has the correct standard form \(7x^2 + 56x = 0\) and the correct factors. However, the original equation was stated to be \(7x^2 = 56x\), so this part is incorrect.
- **Option B**: This option uses a negative instead of the positive value with factors and has incorrect solutions.
- **Option C**: This option states "No GCF" and incorrectly concludes \(x=8\). Thus, it is incorrect.
- **Option D**: This option correctly starts with \(7x^2 - 56x = 0\), factors it correctly as \(7x(x - 8) = 0\), sets each factor equal to zero, and correctly finds the solutions as \(x = 0\) and \(x = 8\).
Thus, **Option D** shows the correct steps to factor out the GCF and solve the quadratic equation.
1. **Put the quadratic in standard form**: First, we need to move all terms to one side of the equation:
\[
7x^2 - 56x = 0
\]
2. **Factor out the GCF**: The GCF of \(7x^2\) and \(-56x\) is \(7x\):
\[
7x(x - 8) = 0
\]
3. **Set each factor equal to zero**:
- From \(7x = 0\), we find \(x = 0\).
- From \(x - 8 = 0\), we find \(x = 8\).
Therefore, the solutions to the equation are \(x = 0\) and \(x = 8\).
Now let's analyze the response options:
- **Option A**: This option has the correct standard form \(7x^2 + 56x = 0\) and the correct factors. However, the original equation was stated to be \(7x^2 = 56x\), so this part is incorrect.
- **Option B**: This option uses a negative instead of the positive value with factors and has incorrect solutions.
- **Option C**: This option states "No GCF" and incorrectly concludes \(x=8\). Thus, it is incorrect.
- **Option D**: This option correctly starts with \(7x^2 - 56x = 0\), factors it correctly as \(7x(x - 8) = 0\), sets each factor equal to zero, and correctly finds the solutions as \(x = 0\) and \(x = 8\).
Thus, **Option D** shows the correct steps to factor out the GCF and solve the quadratic equation.
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