Quiz (Properties of Division)

Show all work and justify each step.

(1) Use long division to divide

    (a)
        
    (b)

(2) Use synthetic division to divide

    (a)
    
    (b)
    
(3) Express the function in the form for the given value of and demonstrate that

    (a) with
    
    (b) with
    
(4) Find a real number such that is a factor of

(5) Find the values for such that is divisible by the linear polynomial

(6) Show that is not a factor of for any real number

(7) Construct a cubic polynomial function with -intercepts of and which passes through the point