Question

Find the quotient of minus, 8, s, to the power 5 , minus, 2, s, to the power 4 , minus, 14, s, cubed, plus, 4, s, squared−8s
5
−2s
4
−14s
3
+4s
2
divided by 2, s, squared2s
2
.

Answer 1

Interpret the divisor as 2s^2. Divide term-by-term:

(-8s^5 - 2s^4 - 14s^3 + 4s^2 - 8s) ÷ (2s^2)
= -4s^3 - s^2 - 7s + 2 + (-8s)/(2s^2).

So the polynomial quotient is -4s^3 - s^2 - 7s + 2 with remainder -8s. As a single rational expression,
(-8s^5 - 2s^4 - 14s^3 + 4s^2 - 8s)/(2s^2) = -4s^3 - s^2 - 7s + 2 - 4/s.