Use the factor theorem to determind if (x+3) is a factor of f(x)=x^4+3x^3-12x^2+100

Question

Use the factor theorem to determind if (x+3) is a factor of f(x)=x^4+3x^3-12x^2+100

Answer 1

Upon cursory inspection, (x+3) is not a factor of the given polynomial because 100 is not evenly divisible by 3.

 

Setting up synthetic division;

 

   −3| 1     3    −12    100

 

              −3       0      36

          1     0   −12   |136  

 

Since the number in the lower right corner is NOT 0, the binomial (x+3) is not a factor of the given polynomial.