Show the supporting work in an easy to read manner Use a sep

Show the supporting work in an easy to read manner. Use a separate piece of paper for scratch work, always show the work YOU DID TO FIND \"a\" FOR THE FORMULAS OF POLYNOMIALS AND RATIONAL FUNCTIONS. Given P(x) = 2(x-1)(.x + 1)^2(x + 2) answer the following. How many turning points (bumps) does it have? Write the of the x-intercept(s). Indicate the multiplicity for each one. Find the coordinates of the P-intercept(s).

Solution

f(x) = 2(x-1)(x+1)^2(x+2)

a) leading term = 2*x*x^2*x = 2x^4

b) Degree = degree of highest term = 4

c) As x ---> infinty

F(x) ----> 2x^4 ----> infinity

d)

As x ---> -infinty

F(x) ----> 2x^4 ---->+ infinity

e) No. of turning point = max degree -1 = 4-1 = 3

f) X intercept : plug y=0

2(x-1)(x+1)^2(x+2) =0

x=1 ; x= -1, -1 ; x= -2

g) P intercept: plog x=0

P(0) = 2(-1)(1)(2) = -4

(0, -4)