Algebra 2 Help

Question

Link : http://imgur.com/a/JZxGv

 

This is a 3 part question so I would be extremely grateful with you could answer the 3 parts. Thanks in advance!!

Answer 1

 

 

  The first part, since it is a third degree polynomial, the can only be one set of complex roots

 

 

 

   Next part is the synthetic division

 

-1 | 1 -7 -1   7
         -1  8  -7
-----------------------
      1 -8  7    0

 

So (X^2 - 8x + 7) results from factoring out (x+1)

 

  ( x   -  7)(x  -  1 ) is the factorization

 

 so the other two roots are 7 and 1

 

Part C is the graph which is left for you.

You can graph it at desmos.com

 

They are asking for a sign chart which 

involves selecting sample values of x

that lie in the intervals between the roots.

 

Again the roots are -1, 1, and 7

 

The intervals are x<-1, -1 < X < 1 and 1 < x < 7.

 

A quick pick and selection of sample values CAN be

 -2,0, and 2 for each interval, respecitively

 

Plugging these in:

 

For x=-2 the polynomial is  (-2)^3 - 7*(-2)^2 - (-2) + 7 = -8 - 28 +2+7 = -27

 

For x = 0 the polynomial is 7

 

for x = 2 the polynomial is  (2)^3 - 7*(2)^2 - (2) + 7 = 8 - 28 - 2 +7 =-15

 

So it up from -27 to 0

       up from 0 to 7

     down from 7 to 0

    down from 0 to -15