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?

The first line reads 3 x superscript 2 baseline plus 2 x minus 8 equals 0. The second line reads 3 x superscript 2 baseline plus 6 x plus left parenthesis negative 4 x right parenthesis minus 8 equals 0. The third line reads left parenthesis 3 x superscript 2 baseline plus 6 x right parenthesis plus left parenthesis left parenthesis negative 4 x right parenthesis minus 8 right parenthesis equals 0. An irregular shape separates the third and fourth lines. The fourth line reads left parenthesis x plus 2 right parenthesis left parenthesis 3 x minus 4 right parenthesis equals 0. The fifth line reads x plus 2 equals 0 or 3 x minus 4 equals 0. The sixth line reads x equals negative 2 or x equals four-thirds.


3x(x+2)−4(x+2)=0


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


x(3x+6)+4(x+2)=0


3x(x+2)−4(x−2)=0

Answer 1

3x(x+2)−4(x+2)=0

Reason: 3x^2+6x = 3x(x+2) and (−4x)−8 = −4(x+2), so the grouped expression becomes 3x(x+2)−4(x+2)=0, which then factors to (x+2)(3x−4)=0.