x-2 is a factor of p(x)=x to the 3rd power -xto the second power +2x-8Use the factor theoem to tell whether the statement is true or not. If the...

p(x)= x^3-x^2+2x-8

(x-2) is a factor??

Solution:

To determine if (x-2) is one of the function's solution, we use the factor theorem. If (x-2) is a factor, then the remainder of dividing p(x) by (x=2) IS ZERO.

Using synthetic division:

   2 l     1      -1       2     -8                     

                     2      2       8

     --------------------------     

            1        1      4      0

The remainder is 0, then (x-2) is a factor of p(x)

Then the statement is true and the other factor is X^2+x+4

Then P(x) = (x-2)(x^2+x+4)