remainder theorem

Question

Use the remainder theorem to find the remainder when f(x) is divided by x+3. Then use the factor theorem to determine whether the x+3 is a factor of f(x).

f(x)=3x^6-27x^4+ x^3- 12

Answer 1

Hi Jessica,

 

We will need to do synthetic division to find the remainder. Set x+3 = 0. x = -3

 

-3| 3  0  -27    1   0   0   -12

   |__-9_ 27_  0_ -3_ 9_ -27_________

    3  -9   0     1   -3   9   -39

 

The remainder is -39.

 

According to the Factor Theorem, you should get a remainder of 0 if x+3 is a factor of f(x). Since we got a remainder of -39, we conclude that x+3 is not a factor of f(x).