Martin solved the quadratic equation 3x2+2x−8=0

Question

. His work is shown below. However, he accidentally spilled ink over the step where he divided by the GCF that he found for each pair. Which of the following options shows the missing part of Martin’s work?

Several lines of equations.

(1 point)
Responses

x(3x+6)+4(x+2)=0
x left parenthesis 3 x plus 6 right parenthesis plus 4 left parenthesis x plus 2 right parenthesis equals 0

3x(x+2)−4(x+2)=0
3 x left parenthesis x plus 2 right parenthesis minus 4 left parenthesis x plus 2 right parenthesis equals 0

3x(x+2)+4(x+2)=0
3 x left parenthesis x plus 2 right parenthesis plus 4 left parenthesis x plus 2 right parenthesis equals 0

3x(x+2)−4(x−2)=0

Answer 1

To solve the quadratic equation \( 3x^2 + 2x - 8 = 0 \) and to determine the missing part of Martin's work where he divided by the GCF (Greatest Common Factor), we need to look for the correct factorization of the equation.

Starting from the original equation:

1. We can factor the quadratic expression. We will need to identify pairs of terms and see if there is a common factor.

The equation can be rearranged as:

\[ 3x^2 + 6x - 4x - 8 = 0 \]

2. Next, we can group the terms:

\[ (3x^2 + 6x) + (-4x - 8) = 0 \]

3. Now we can factor out the GCF from each group:

\[ 3x(x + 2) - 4(x + 2) = 0 \]

4. Now, we notice that \((x + 2)\) is a common factor:

\[ (3x - 4)(x + 2) = 0 \]

In terms of picking from the provided responses, the step that Martin might have accidentally missed after identifying the GCF from each pair would be this:

\[ 3x(x+2) - 4(x+2) = 0 \]

So, the correct response showing the missing part of Martin's work would be:

3x(x+2) - 4(x+2) = 0