Answer:

In order to find Q(x) and R(x) using synthetic division, we divide the polynomial P(x) by the linear polynomial D(x).

The dividend polynomial is: P(x) = x^5 - x^4 - 6x^3 + 4x^2

The divisor polynomial is: D(x) = -3x + 1

Performing synthetic division:

1/3 | 1 -1 -6 4 0 0

| 1/3 0 -6/3 -2/3 2/3

-----------------------------------

1 1/3 -18/3 -2/3 2/3 0

The quotient polynomial Q(x) is: Q(x) = x^4 + (1/3)x^3 - (18/3)x^2 - (2/3)x + (2/3)

The remainder polynomial R(x) is: R(x) = 0

Hence, Q(x) = x^4 + (1/3)x^3 - (18/3)x^2 - (2/3)x + (2/3) and R(x) = 0.