What are the solutions?

x3-8x²-x+8=0

Question 5 options:

(8,1,-1)

(8,1)

(8,1-1,0)

In order to answer this, we must factor x3-8x2-x+8=0

We can make 2 pairs of 2 terms in order to make the factoring easier,

(x3-8x2) + (-x+8) = 0

Now we can begin to factor each pair of terms one at a time,

x2 (x-8) - (x-8) = 0

We can see that we have 2 (x-8) s so that is our common and we have x2-1 (we can't see the 1 because anything times 1 equals itself so we don't need to put it there).

(x2-1) (x-8) = 0

Expand,

(x+1) (x-1) (x-8) = 0

In order for 0=0, we must find values of x that will make 0=0

When x=1

(1+1) (1-1) (1-8) = 0

2 x 0 x - 7=0

0=0

When x=8

(8+1) (8-1) (8-8) = 0

9 x 7 x 0=0

0=0

When x=-1

(-1+1) (-1-1) (-1-8) = 0

0 x - 2 x - 9=0

0=0

Therefore, the answer is x=8,1,-1 or (8,1,-1)