Quiz (Zeros of Polynomials)

Show all work and justify each step.

(1) Find the zeros of and state the multiplicity of each. Sketch the graph of each function

    (a)
    
    (b)

(2) Find a polynomial of degree 7 such that and are both zeros of multiplicity 2, 0 is a zero of multiplicity 3, and Sketch the graph of

(3) Construct a polynomial function with the stated properties.

    (a) Fifth degree, only real coefficients, 0 is the only real zero, is a zero of multiplicity 1, leading coefficient is 1.
    
    (b) Fourth degree, only real coefficients, -intercepts are 0 and 6, is a zero, leading coefficient is 3.
    
    (c) Fifth degree, is a zero of multiplicity 2, another integer is a zero of multiplicity 3, and -intercept is leading coefficient is 1.