Originally Posted by

**nandokommando** (x) = x^5 - 7x^4 + 3x^3 - 2x^2 + 5x - 1. Then P(x) = (x - 2)Q(x) + R. If so, Q(x) =

These problems always give me a hard time, can anyone explain it to me? The answer is x^4 - 5x^3 - 7x^2 - 16x - 27 but I have no idea how to get there.

Hi nandokommando,

tells you that the dividend **P(x)** = the divisor **(x-2)** times the quotient **Q(x)** plus the remainder **R**. This is the Remainder Theorem.

Now, either use long division or synthetic division to determine the depressed polynomial **Q(x)** after dividing by **(x - 2).**

Synthetic Division:

Code:

2 ] 1 -7 3 -2 5 1
-- 2 -10 -14 -32 -54
---------------------------
1 -5 -7 -16 -27 -53

The depressed polynomial is