Question

Question

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

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

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 minus 2 right parenthesis equals 0
Remaining Attempts : 3
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Answer 1

To solve the quadratic equation \(3x^2 + 2x - 8 = 0\), Martin first recognizes that he can group the terms in a way that allows for factoring.

From the structure of the equation, he is likely trying to factor by grouping. The format \(3x(x+2) - 4(x+2) = 0\) indicates that he correctly factored out a common term from parts of the equation. The common term here is \(x + 2\).

Thus, the correct missing step would involve factoring out the common factor, which leaves us with:

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

So, given the choices provided in the question, the line of equation that Martin likely wrote before the one you shared is:

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

This corresponds to the first option:

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

This line indicates the correct grouping and shows the factorization step required to progress in solving the quadratic equation.