Germany | Math Olympiad Question | You should be able to solve this!

Maths Olympiads are held all around the world to recognise students who excel in maths. The test is offered at many grade levels and provides them with numerous possibilities to win certifications, awards, and even scholarships for higher studies

[spadetrotter]

If it’s divisible by x+1, then the remainder is zero.

[SGTsparty]

confused. i thought remainder was was a division issue, all that happened here is that there was an arbitrary substitution (from the point of view of the question, so how is this a remainder? Also, how can you just say X+1=0? The number of assumptions

[scopoulis]

IMHO, when we say that a polynomial q(x) divides a polynomial p(x) we do not necessarily mean that q(x) is a FACTOR of p(x) (i.e we don't mean that q(x) divides EXACTLY p(x) ) therefore the expression "is divisible by q(x)" implies that we can just carry out the division (i.e that the degree of q(x) is not greater than the degree of p(x), which in our case was obvious making the declaration about the divisibility by (x+1) either redundant or ... on purpose disoriantating ). It does not mean that the remainder is zero. The remainder can be EITHER a polynomial with degree one less than the degree of q(x) OR the zero polynomial . More specifically, the remainder theorem states that when a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a), because p(x) = (x - a) · q(x) + r => p(a) = 0 + r => r = p(a). Therefore I believe the answer is correct. It's not that nice to shoot the instructor! 😊

[samwong]

You have mixed up the meaning of "is divisible" and "is divided", unfortunately. (Note that P(x) is NOT divisible by (x-1)). People trying to teach in Youtube must know their own limitation in order to contribute.