how do you find x intercept for y= -x^3 -x +2

Question

how do you find the x intercept

Answer 1

By inspection you can see that if x=1, y=-1-1+2=0, so x=1 is an x-intercept.

To find more x intercepts (if any) divide by the zero 1 using synthetic division:

1 | -1  0  -1   2

     -1 -1 -1 | -2

    -1  -1 -2 |  0 =-x²-x-2.

x²+x=-2, x²+x+¼=-2+¼, (x+½)²=-7/4 which has no real solutions (no real square root of a negative number). So x=1 is the only x-intercept.