Jacob believes that for all positive integers n3+n+2n^3 + n + 2n3+n+2 is a multiple of kkk.
The value n=4n = 4n=4 is a counter example to Jacob’s belief.
Which value of k k\,k shown below makes n=4n = 4n=4 a counter example to Jacob’s belief?
k=2k=4k=5k=7 k = 2 \quad k = 4 \quad k = 5 \quad k = 7 k=2k=4k=5k=7k=2k = 2k=2
k=4k = 4k=4
k=5k = 5k=5
k=7k = 7k=7
257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.