24.9k views
0 votes
3. Determine which of the following functions below have (x + 6) as a factor.

Select all that apply.
( 2x3 - 19x2 - 7x + 294
0 4x3 + 11x2 - 75x + 18
3x3 + 34x2 + 61% -- 210
x3 + 6x2 + 11x + 6
10x3 + 53x2 - 41x + 6

User Atural
by
8.2k points

1 Answer

5 votes

Answer:

B, C, and E

Explanation:

Since x+6 has the root x=-6, we should be getting 0 after plugging it into each expression by the Remainder Theorem:


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 <-- remainder isn't 0; A is out


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<-- remainder IS 0; B is a correct choice


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<-- remainder IS 0; C is a correct choice


x^3 + 6x^2 + 11x + 6\\(-6)^3+6(-6)^2+11(-6)+6\\-216+6(36)-66+6\\-216+216-60\\-60<-- remainder isn't 0; D is out


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<-- remainder IS 0; E is a correct choice

Thus, the correct choices are B, C, and E.

User Maelish
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories