Help me Build a Polynomial

Question

Build a 4th Degree Polynomial with four Zeros as follows:Two rational zeros(at least one is a fraction)and Either Two Irrational Zeros of the form (a+bi)

Construct a Factored form the Zeros

Analyze the Factored Form and Sketch a Graph

List all Possible Rational Zeros

Use Synthetic Division to Depress Polynomial to a Quadratic

Discuss the realtionship of the factors

Answer 1

(2x-1)(x+1) (x + sqrt(2))(x - sqrt(2)) =

(2x^2 +x -1) (x^2 - 2)

finish it