Answer:
B, C, and E
Step-by-step explanation:
Since x+6 has the root x=-6, we should be getting 0 after plugging it into each expression by the Remainder Theorem:
[tex]2x^3-19x^2-7x+294\\2(-6)^3-19(-6)^2-7(-6)+294\\2(-216)-19(36)+42+294\\-432-684+42+294\\-780[/tex] <-- remainder isn't 0; A is out
[tex]4x^3 + 11x^2 - 75x + 18\\4(-6)^3+11(-6)^2-75(-6)+18\\4(-216)+11(36)+450+18\\-864+396+468\\-864+864\\0[/tex]<-- remainder IS 0; B is a correct choice
[tex]3x^3 + 34x^2 + 61x - 210\\3(-6)^3+34(-6)^2+61(-6)-210\\3(-216)+34(36)-366-210\\-648+1224-366-210\\576-366-210\\210-210\\0[/tex]<-- remainder IS 0; C is a correct choice
[tex]x^3 + 6x^2 + 11x + 6\\(-6)^3+6(-6)^2+11(-6)+6\\-216+6(36)-66+6\\-216+216-60\\-60[/tex]<-- remainder isn't 0; D is out
[tex]10x^3 + 53x^2 - 41x + 6\\10(-6)^3+53(-6)^2-41(-6)+6\\10(-216)+53(36)+246+6\\-2160+1908+252\\-252+252\\0[/tex]<-- remainder IS 0; E is a correct choice
Thus, the correct choices are B, C, and E.
