Question

Divide using synthetic division, and write a summary statement in fraction form. 2x^5-x^4-3x^2-x+5/x-1

Answer 1

(2x^5 - x^4 - 3x^2 - x + 5) / (x - 1)
Note: The x^3 term is missing. Introduce 0x^3 and the coeficients are:
2 -1 0 -3 -1 +5

1 2 -1 0 -3 -1 +5
2 1 1 -2 -3
--------------------------
2 1 1 -2 -3 2

Quotient = 2x^4 + x^3 + x^2 - 2x - 3; Remainder 2

(2x^5 - x^4 - 3x^2 - x + 5) / (x - 1) = 2x^4 + x^3 + x^2 - 2x - 3 + 2 / (x - 1)