Please show me the work and show me the answer. Thank you.

MATH 108 Problem Set 2: Section 2.4-2.7 Section 2.4: Dividing Polynomials; Factor/Remainder Theorem 1) Divide the following using long division. State the quotient and remainder. x*+2x' -4x' -5x-6 r+x-2 2) Divide f(x) = x* -5x +5x3 +5x-6 by x-2 a) Quotient: b) Remainder: c) Is x-2 a factor of f (x) ? Why or why not? d) If the answer to part cis yes, then use the results of your division problem to factor f (x) and find all of the zeros Section 2.5: Zeros of a Polynomial Function 3) For the polynomial equation: 2x -5x- -6x+4=0 a) List all of the possible rational zeros b) Use synthetic division to test the possible zeros until you find a zero that works c) Use the quotient from part b to find any remaining zeros of the polynomial. 4) For the polynomial equation: x* -2x- -16x-15=0 a) List all of the possible rational zeros b) Use synthetic division to test the possible zeros until you find a zero that works c) Use the quotient from part b to find any remaining zeros of the polynomial. 5) Use the linear factorization theorem to find the equation for the no degree polynomial function with real coefficients satisfying the given conditions n = 3 1 and Si are zeros f(-1) =-104Section 2.6: Rational Function 6) Use the graph of the below rational function to complete each statement. x = 2 4 3 1 y = 0 (-2, 0) (3, 0) -5 -4 -3 -2 +1 0 1 COT 4 5 -1 (0, -2) -3 -4 -5 a) As x-1", f(x)- b) As x- -1, f(x) - c) As x - 2", f(x)-> d) As x -> 2", f(x)- e) As x - 0', f(x)-> f) As x-> 0', f(x) - 8) As x-> 3", f(x)-> h) As x-> 3", f(x)-> i) As x -> -00, f(x) > i) As x -+ 00, f(x) ->7) For the following rational functions 1 a) R(x) = +1 (x-3)- Domain: Range: Vertical Asymptote: . . . . Horizontal Asymptote: Graph this function using transformations. Plot all asymptotes as dashed lines on the graph b) R(x) = _-2 Domain: Range: . . . . . Vertical Asymptote: Horizontal Asymptote: Graph this function using transformations Plot all asymptotes as dashed lines on the graph 8) Graph the rational function f(x) =- 4x- x- +1 using the seven step strategy a) Domain: b) Vertical Asymptotes: Holes (if any): d) Horizontal Asymptote: e) Y-Intercept f) X-Intercept(s) g) Plot points between each x-intercept and vertical asymptote and use your results to sketch the graph of the function