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
1 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
2 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=8Put 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
3 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
4 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
Responses
1 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
2 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=8Put 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
3 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
4 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 solve the quadratic equation \(7x^2 = 56x\), we will follow the correct steps to rewrite the equation, factor out the greatest common factor (GCF), set each factor to zero, and find the solutions.
1. **Put the quadratic in standard form**: First, we need to rewrite the equation as follows:
\[
7x^2 - 56x = 0
\]
2. **Factor out the GCF**: The GCF of the terms \(7x^2\) and \(-56x\) is \(7x\), so we factor it out:
\[
7x(x - 8) = 0
\]
3. **Set each factor equal to zero**:
\[
7x = 0 \quad \text{and} \quad x - 8 = 0
\]
- From \(7x = 0\), we get \(x = 0\).
- From \(x - 8 = 0\), we get \(x = 8\).
4. **The solutions are**:
\[
x = 0 \quad \text{and} \quad x = 8
\]
Now, let's compare this with the provided options:
- **Option 1** is incorrect.
- **Option 2** is correct: The steps are accurately described, leading to the correct solutions of \(x = 0\) and \(x = 8\).
- **Option 3** is incorrect: It states that one solution is \(x = -7\), which is wrong.
- **Option 4** is incorrect: The equation is incorrectly written as \(7x^2 + 56x = 0\), and it has incorrect solutions.
Thus, the correct response is **Option 2**.
1. **Put the quadratic in standard form**: First, we need to rewrite the equation as follows:
\[
7x^2 - 56x = 0
\]
2. **Factor out the GCF**: The GCF of the terms \(7x^2\) and \(-56x\) is \(7x\), so we factor it out:
\[
7x(x - 8) = 0
\]
3. **Set each factor equal to zero**:
\[
7x = 0 \quad \text{and} \quad x - 8 = 0
\]
- From \(7x = 0\), we get \(x = 0\).
- From \(x - 8 = 0\), we get \(x = 8\).
4. **The solutions are**:
\[
x = 0 \quad \text{and} \quad x = 8
\]
Now, let's compare this with the provided options:
- **Option 1** is incorrect.
- **Option 2** is correct: The steps are accurately described, leading to the correct solutions of \(x = 0\) and \(x = 8\).
- **Option 3** is incorrect: It states that one solution is \(x = -7\), which is wrong.
- **Option 4** is incorrect: The equation is incorrectly written as \(7x^2 + 56x = 0\), and it has incorrect solutions.
Thus, the correct response is **Option 2**.