Final answer:
The polynomial is not divisible by x-3.
Step-by-step explanation:
To determine if the polynomial f(x)=6x⁴ -2x² +3x+1 is divisible by x-3, we can use synthetic division.
We set up the synthetic division table with the coefficients of the polynomial:
3 | 6 0 -2 3 1
Using synthetic division, we divide each coefficient by 3:
3 | 6 0 -2 3 1
18 54 144 441 1326
The last entry in the bottom row is the remainder. Since the remainder is not zero, the polynomial is not divisible by x-3.