# Resources tagged with: Polynomial functions and their roots

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Broad Topics > Coordinates, Functions and Graphs > Polynomial functions and their roots ### Common Divisor

##### Age 14 to 16Challenge Level

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

##### Age 14 to 16Challenge Level

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. . . . ### Two Cubes

##### Age 14 to 16Challenge Level

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. . . . ### Root to Poly

##### Age 14 to 16Challenge Level

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

##### Age 14 to 18Challenge Level

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

##### Age 14 to 18Challenge Level

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