Synthetic division is the easiest to try and explain in this forum. If x - 5 is a factor of that polynomial, when you divide you will get a 0 remainder. If x - 5 = 0, then x = 5. That will be the number we put inside the little box using synthetic division. 5∫ 3 0 0 -4
____ 15__125___625 That's the synthetic division.
3 15 125 621
Hopefully it retains it formatting. Bring down the first 3 and multiply it by 5 to get 15 and put that 15 up under the first 0 (place holder for the missing x^2 term). Add 0 + 15 to get 15. Multiply 5 by 15 to get 125. Put the 125 up under the second 0 (place holder for the missing x term) and add to get 125. 5 * 125 = 625. And then subtract 4 from that to get a remainder of 621. Obviously x - 5 is not a factor!
