Move the slider for the value of k to see what happens to the graph of f(x)=2x5+x4-3x2+k.

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Answer the following.
1)Use the slider to find a value of k so that f(x)=2x^5+x^4-3x^2+k has three distinct real roots.

2) Find by hand all the zeros (including complex ones) of the polynomial f(x) when k=0.

3) Find the multiplicity of each zero.

4) Use part (2) and (3) to completely factor f(x) when k=0.

5) Change the expression for f(x) to another fourth or fifth degree polynomial and explore with the applet. Summarize your findings.

by Reva Narasimhan, Created with GeoGebra