If the third degree polynomial x3 - 10x2 + 12x + 72 can be factored to (x + 2) · y2, what is y in terms of x ?
A. x - 6
B. x - 3
C. x - 1
D. x + 1
Answer:A
If the third degree polynomial x3 - 10x2 + 12x + 72 can be factored to (x + 2) · y2, what is y in terms of x ?
A. x - 6 B. x - 3 C. x - 1 D. x + 1
Explanation: A Given that all of the answer choices are possible values for y, plug in the answers. In (A), y = x - 6. Plug this value into (x + 2)y2 to get (x + 2)(x - 6)(x - 6). Multiply the last two factors together to get (x + 2)(x2 - 12x + 36). Multiply the two resulting factors together to get x3 - 12x2 + 36x + 2x2 - 24x + 72. Combine like terms to get x3 - 10x2 + 12x + 72. This is the same as the third degree polynomial in the question. Therefore, the correct answer is (A).