Question

What are the solutions?

Answer 1

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)