Question

A polynomial f (x) has the given zeros of 8, –1, and –3.

Part A: Using the Factor Theorem, determine the polynomial f (x) in expanded form. Show all necessary calculations. (3 points)

Part B: Divide the polynomial f (x) by (x2 – x – 2) to create a rational function g(x) in simplest factored form. Determine g(x) and find its slant asymptote. (4 points)

Part C: List all locations and types of discontinuities of the function g(x). (3 points)

Answer 1

The answer is "$\bold{x^3-4x^2-29x-24, y=x-3,\ and\ x=2}$" and following are the complete solution to the given parts:

For point A)$\to \bold{f(x)=(x-8)(x+1)(x+3)=(x^2-7x-8)(x-8)=(x^3-4x^2-29x-24)}$For point B)

$\to \bold{x^2-x-2=(x-2)(x+1)}\\\\\to \bold{g(x)=\frac{(x-8)(x+1)(x+3)}{(x-2)(x+1)}}$

When  $x \neq -1$ then  

$\to \bold{g(x)=\frac{(x-8)(x+3)}{x-2}}\\\\\to \bold{\lim_{n \to \infty} \frac{g(x)}{x}}$

So  

For point C)

It is discontinuity when a $\bold{x=2}$ that is a vertical asymptote.

Learn more:

brainly.com/question/24520259

Answer 2

Answer:

Part A:

x^3 - 4x^2 - 29x -24

(x + 1)(x - 8)(x + 3)

Part B.

(x + 1)(x - 8)(x + 3) / x^2 - x - 2= (x + 3)(x - 8) / x - 2

g(x)=  (x + 3)(x - 8) / x - 2= y= x - 3

Part C.

x=2.

Step-by-step explanation:

See images for more information, it wouldn't let me post it.