Hello forum.

I have a homework which consists of 40 exercises, but I don't understand it, can you please teach me how to solve these 8 exercises so I could use them as guide to do my H.W, Thanks

1-For the following polynomial funcion f:

f(x)= (x-4)(x+2)^2(x-2)

A- Find the x and y intercepts of F

B Determine whether the graph of f crsses or toches the x axis at each x intercept

C- End behavior. Find the power function that the graph of f resembles for large values of |x|

D- Determine the maximum number of turning points on the graph of f.

E- Use the x intercept(s) to find the intervals on which the graph of f is above and bellow the x axis.

F- Plot the points obtained in parts A and E and use the ramaining information to connect them with a smooth, continuos curve.

2- Find the domain of the given rational functions. Find any vertical, horizontal or oblique asymptotes. Graph the given rational function.

a r(x)=3x^3/x^2-2x-1

b f(x)=)x^2-10x-12/x^2+x-6

c f(x) =1/x-2

d f(x)= x-1/x-2

3-aUse synthetic division to find the quotient q(x) and remainder r(x) when f(x) is divided by g(x). is factor of f? f(x) =x^4-x^2+2x+2 g(x) =x+1

b= use synthetic division to find f(1/2)

c= is (X+1/2) a factor of the function f

4- list all the potential rational zeros of the function f, do not attemtp to find the zeros

f(x) = 12x^8-x^7+6x^4-x^3+x-3

5= use the rational zeros theorem to find all the zeros of each polynomial function. Use the zeros to factor F over the real numbers

f(x) =x^3+2x^2-5x-6

6form a polynomial f(x) with real coheficients having the giving degree and zeros .Degree 3; zeros:1,-4+i

7-Solve the given equation in the complex number system. x^4+5x^3+2x^2-x+6=0 hint, find p(-3) and p(-2)

8- use the intermediare value theorem to show that each of these polynomials has a zero in the given interval

a f(x) =8x^4-2x^2+5x-1 {0,1}

b f(x) =x^4+8x^3-x^2+2 {-1,0}

thank you.