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Sagot :
Given data:
The x-intercepts given are 4 and -2.
Substitute 0 for y in the first option.
[tex]\begin{gathered} 0=3x^2-10x-8 \\ 3x^2-12x+2x-8=0 \\ 3x(x-4)+2(x-4)=0 \\ x=4,\text{ -}\frac{2}{3} \end{gathered}[/tex]Substitute 0 for y in the second option.
[tex]\begin{gathered} 0=x^2+2x-8 \\ x^2+2x-8=0 \\ x^2+4x-2x-8=0 \\ x(x+4)-2(x+4)=0 \\ (x-2)(x+4)=0 \\ x=2,\text{ -4} \end{gathered}[/tex]Substitute 0 for y in the third option.
[tex]\begin{gathered} 0=3x^2-2x-8 \\ 3x^2-2x-8=0 \\ 3x^2-6x+4x-8=0 \\ 3x(x-2)+4(x-2)=0 \\ (x-2)(3x+4)=0 \\ x=2,\text{ -}\frac{4}{3} \end{gathered}[/tex]Substitute 0 for y inlast option.
[tex]\begin{gathered} 0=x^2-2x-8 \\ x^2-4x+2x-8=0 \\ x(x-4)+2(x-4)=0 \\ (x-4)(x+2)=0 \\ x=4,\text{ -2} \end{gathered}[/tex]Thus, option (D) is correct.
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