Birthday polynomial project for birthdate 02/03/2002

Question

Create polynomial using birthday 02/03/2002. Degree must be > 2, end behavior, amount of real and imaginary zeros, relative mins Max's, find all zeros, find all zeros, intervals of increasing and decreasing, x and y intercepts

Answer 1

x^3 - 2x^2 - 2x + 2^2

=x^2 - 2x^2 - 2x + 4

x^2(x-2) - 2(x-2)

(x^2 - 2)(x-2)

3 real zeros x=2, x = sqrt(2) , x = -sqrt(2)

end behavior blows up as x tends to infinity and

blows down and x tends to negative infinity