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,
$\displaystyle P(x)=(x-2) \cdot Q(x) + R$ 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 $\displaystyle x^4-5x^3-7x^2-16x-27+\frac{-53}{x-2}$