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
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=−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
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=−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
C .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
D .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 x−8=0
Factor out the GCF No GCF
Set each factor equal to zero x−8=0
The solutions are x=8
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=−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
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=−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
C .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
D .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 x−8=0
Factor out the GCF No GCF
Set each factor equal to zero x−8=0
The solutions are x=8
Answers
GPT-4o mini
To solve the quadratic equation \( 7x^2 = 56x \), we first need to rearrange it into standard form:
1. Move all terms to one side:
\[
7x^2 - 56x = 0
\]
2. Next, factor out the greatest common factor (GCF), which is \( 7x \):
\[
7x(x - 8) = 0
\]
3. Set each factor equal to zero:
\[
7x = 0 \quad \text{and} \quad x - 8 = 0
\]
4. Solve for \( x \):
- From \( 7x = 0 \), we get \( x = 0 \).
- From \( x - 8 = 0 \), we get \( x = 8 \).
Thus, the solutions are \( x = 0 \) and \( x = 8 \).
Looking at the provided options:
- **Option A** incorrectly states the solutions as \( x = -7 \) and \( x = 8 \).
- **Option B** incorrectly begins with \( 7x^2 + 56x = 0 \) and gives incorrect solutions \( x = -8 \) and \( x = 0 \).
- **Option C** correctly puts the quadratic in standard form, factors it accurately, and gives mistaken solutions \( x = 0 \) and \( x = 8 \) (the correct solutions are fine, but the format is less informative).
- **Option D** correctly describes the steps and keeps the notation clear, providing the correct solutions \( x = 0 \) and \( x = 8 \).
- The last option incorrectly states that there is no GCF.
The correct answer, in terms of clarity and accuracy with all steps shown, is **Option D**.
1. Move all terms to one side:
\[
7x^2 - 56x = 0
\]
2. Next, factor out the greatest common factor (GCF), which is \( 7x \):
\[
7x(x - 8) = 0
\]
3. Set each factor equal to zero:
\[
7x = 0 \quad \text{and} \quad x - 8 = 0
\]
4. Solve for \( x \):
- From \( 7x = 0 \), we get \( x = 0 \).
- From \( x - 8 = 0 \), we get \( x = 8 \).
Thus, the solutions are \( x = 0 \) and \( x = 8 \).
Looking at the provided options:
- **Option A** incorrectly states the solutions as \( x = -7 \) and \( x = 8 \).
- **Option B** incorrectly begins with \( 7x^2 + 56x = 0 \) and gives incorrect solutions \( x = -8 \) and \( x = 0 \).
- **Option C** correctly puts the quadratic in standard form, factors it accurately, and gives mistaken solutions \( x = 0 \) and \( x = 8 \) (the correct solutions are fine, but the format is less informative).
- **Option D** correctly describes the steps and keeps the notation clear, providing the correct solutions \( x = 0 \) and \( x = 8 \).
- The last option incorrectly states that there is no GCF.
The correct answer, in terms of clarity and accuracy with all steps shown, is **Option D**.