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

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
Skip to navigation

GPT-4o mini · Answer

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 : 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.