Expert: Sherry Wallin - 8/24/2010

Question
(x^3-4x^2+x+6)/ (x+1)

Answer
Kayla~

What is the question?? I can assume you need to factor the top and see if there is a factor of x+1 in the numerator that you can cancel with the denominator but you need to state a question when asking for help.

There are many ways to approach this problem but knowing what level of math you are in would help immensely because the easiest to check but probably the highest mathematically would be to see if f(-1) = 0 and if it does then we know that x+1 is a factor of the numerator and then we can divide x+1 into the numerator:

f(-1) = (-1)^3 - 4(-1)^2 +(-1) + 6 = -1 - 4 -1 + 6 = 0 thus x + 1 is a factor of  x^3-4x^2+x+6. Now do long division to find the factorization. I prefer to use synthetic division:

-1 |1   -4   1   6
       -1   5  -6
   ______________
   1   -5   6   0  -> (x+1)(x^2 -5x + 6) but

(x^2 -5x + 6) factors as (x-2)(x-3)

so (x^3-4x^2+x+6)/ (x+1) = (x+1)(x-2)(x-3)/(x+1) = (x-2)(x-3)

Math Prof