(x^5-3x^4-5x^3+x^2-x+35)/(x+2)

Question

divide by using synthetic division

Answer 1

Divide by the root, that is, x+2=0, x=-2, so the root is -2:

-2 | 1 -3  -5    1  -1    35

      1 -2 10 -10 18 | -34

      1 -5   5   -9 17 |     1 remainder.

Quotient is x⁴-5x³+5x²-9x+17.

If the dividend had been x⁵-3x⁴-5x³+x²-x+34 there would have been no remainder.