2 out of 3
Can you find the value of this function involving algebraic fractions for x=2000?
2 out of 3
By proving these particular identities, prove the existence of general cases.
3 out of 3
A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
3 out of 3
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
3 out of 3
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.
