Question

If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem

Answer 1

The function is: f ( x ) = x³ - 2 x² - 68 x - 120
If f ( - 2 ) = 0, we have to divide this equation by: ( x + 2 )
( x³ - 2 x² - 68 x - 120 ) : ( x + 2 ) = x² - 4 x - 60
- x³ - 2 x²
--------------
       - 4 x² - 68 x - 120
         4 x² + 8 x
  ---------------------------
                - 60 x - 120
                  60 x + 120
                -----------------
                               0
After that for a function: f ( x ) = x² - 4 x - 60;   f (  - 6 ) = 0
( x² - 4 x - 60 ) : ( x + 6 ) = x - 10
 -x² - 6 x
-----------------
        - 10 x - 60
          10 x + 60
          -------------
                      0
Answer:
       C )    ( x - 10 ) ( x + 2 ) ( x + 6 )