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=0
and x=8
B. 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

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

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
C. 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

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=−8
and x=0

Answer 1

To factor out the GCF and solve the quadratic equation \( 7x^2 = 56x \), we start by rearranging the equation into standard form:

1. **Put the quadratic in standard form**:
\[
7x^2 - 56x = 0
\]

2. **Factor out the GCF** (Greatest Common Factor):
The GCF of \( 7x^2 \) and \( 56x \) is \( 7x \), so we can factor it out:
\[
7x(x - 8) = 0
\]

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:
\[ x = 8 \]

So the solutions are:
\[ x = 0 \quad \text{and} \quad x = 8 \]

The correct response that shows these steps is **Option A** and **Option B** (they are identical).

Therefore, both **A** and **B** are correct:
- They both correctly detail the full process to put the equation in standard form, factor out the GCF, set the factors to zero, and find the appropriate solutions.

Responses **C** and **D** contain inaccuracies in the steps that do not lead to correct solutions to the equation.