Question

Factroise x^3-x^2+ax+x-a-1

Answer 1

Answer:

 factors : (x - 1) and (x²  + a +1)

Step-by-step explanation:

Given expression  f(x) =x³ - x² + a x + x - a - 1

method 1:

    f(x) = x² (x - 1) + x (a +1) - (a+1)

          = x² (x - 1) + (x - 1) (a + 1)

           =  [x² + a + 1] (x - 1]

  If a is negative and is less than  -1, then  the factor x² +a+1 can be broken into two factors :  (x + √(-1-a)  and (x - √(-1-a)

Method 2:

  f(x) = 0  if  x = 1,  by simple observation of the expression.

   So x-1 is a factor.

   Using the method of expression division, we find that  x² + a + 1 is the other factor.