The table represents the start of the division of 15x3 + x2 - 3x + 2 by 3x + 2. /3x/ 2/___/__/__/ <--- this row shaded___/__/__/___/__/__/ Which terms belong to one of the shaded cells inside the table? Check all that apply. a. -9x^2 b. -6x c. x^2 d. 5x^2 e. 15x^3

Answer: Option d. [tex]15x^3[/tex] is right.Explanation: For determining all the term in the shaded reason we must divide [tex]15x^3+x^2-3x+2[/tex] by [tex]3x-2[/tex]since 3x-2=0 then x=2/3 and 2/3 is the root of the [tex]15x^3+x^2-3x+2[/tex] because [tex]15x^3+x^2-3x+2=0[/tex] at 2/3 then it will completely divided by 3x-2So, we can right,  [tex]15x^3+x^2-3x+2=( 5x^2-3x+1)(3x-2)[/tex]after comparing this to the shaded reason in first row we will get 5x^2, -3x, and 1 .Thus, option d .[tex]5 x^2[/tex] will be right.