What is remainder when x^2 - 4x + 11 is divided by 3 (1) x+1 is divisible by 3 (2) x-2 is divisible by 3

I'll go with D. A) Since (x+1) is divisible by 3, we know that (X+1)(X-5) is divisible by 3. This gives us x^2-4x-5. This is divisible by 3. To get the equation in the question we need to add 16. Since 15 is divisble by 3, the R=1. Sufficient. B)Similar logic to above. (x-2)(x-2) is divisible by 3. X^2-4x+4 is divisible by 3. We need to add 7 to get the original equation. Since 6 is divisible by 3, R=1.

Nice work, 720Dreaming. The answer is D. Here's my full solution as well: (1) one option is to plug in 2 values (or 3 to provide a little more certainty) for x such that x+1 is divisible by 3 (e.g., x=2, 5, 8 etc) and check whether each value of x yields the same remainder when x^2 - 4x + 11 is divided by 3 (2) Recognize that this information is the same information that was provided in (1). If x+1 is divisible by 3, then it must follow that x-2 is divisible by 3. When (1) and (2) provide identical information, then the correct answer must be either D or E. Let's see when the correct answer is D. When we look at the expression x^2 - 4x + 11, we can see that it’s ALMOST possible to factor out x-2 from this expression. In fact (x-2)^2 = x^2 + 4x + 4 So, we can rewrite x^2 - 4x + 11 as x^2 + 4x + 4 +7, which is the same as (x-2)^2 +7, which is the same as (x-2)^2 +6 + 1 Since x-2 is divisible by 3, it must be true that (x-2)^2 is divisible by 3 and it follows that (x-2)^2 +6 is divisible by 3 So, (x-2)^2 +6 + 1 (aka x^2 - 4x + 11) must have a remainder of 1 when divided by 3