There are **6** NRICH Mathematical resources connected to **Polynomial functions and their roots**, you may find related items under Coordinates, Functions and Graphs.

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Quadratic graphs are very familiar, but what patterns can you explore with cubics?

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Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

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Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

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This problem challenges you to find cubic equations which satisfy different conditions.

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Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

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Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to. . . .