use the factor theorem to determine whether (x-3) is a factor of f(x)=x^4+12x^3+6x+27

use the factor theorem to determine whether (x-3) is a factor of f(x)=x^4+12x^3+6x+27

Answer

(x)=x  ⁴  given that x-3 is a factor of expression

use remainder theorem

put x  - 3  = 0

we get x = 3

plug 3 in place of x in the given value of f (x)

f(x)=x⁴+ 12x³ + 6x + 27

f(3)=(3)⁴+12(3)³+6(3)+27.

     = 81+ 324 + 18 + 27

     = 430

here 430 is not equal to 0 so that  Hence x -3 is not a factor of f(x)=x^4+12x^3+6x+27