Which of the following tables shows the correct steps to factor out the GCF and solve the quadratic equation 7x2=56x?(1 point)

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

GPT-4o mini · Answer

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**.