Andy C. answered • 08/14/17

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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

-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