1. Let f(x) =-x(x-3)(x+2)(x-5) (a) What is the degree of the polynomial? (b) Find all the zeros of this polynomial and state their multiplicities. (c) Use this information to sketch the graph of f. 2. (a) Find a polynomial f(x) of degree: 3 with zeros: -5, -4, and 1 such that f(-6) = 28. (b) Find the equation of the polynomial f(x) graphed on the right. The degree of this polynomial is 6 and f(1) =100. Leave the answer in factored form. WW. 3. Find all solutions of the following equations by hand (without using a calculator): x -8x3 +8x+24 =0 given that 6 is a solution of this equation. 4. Find the quotient and the remainder if f(x) = 3x' +4x3 + x+7 is divided by p(x) = x' +1 5. Graph each of the following rational functions. List any asymptotes, holes, and the x- intercepts and the y-intercepts. (a) f(x) = 3x-2 x+4 (b) f (x ) = 2x- -x-3 x-2 (c) f(x )= 2x* +4x-48 x2 + 3x -10 6. Sketch the graph of each function using the following steps: (i) Identify and sketch the graph of the parent function (ii) Indicate how the parent graph is transformed (iii) Sketch the graph of the function, including the asymptote. (a) f(x) = 2"'-4 (b) f(x)=-2log, (x+3)