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# Question about Quotient and remainder

Use synthetic division to find the quotient q(x) and remainder r

(5 x 3 - 21 x 2 - 103) / (x - 5)

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SOLUTION

Ramp length 8ft
N

F
Mgsinθ 20 inches = 1.67ft

Mgcosθ
θ Mg

Let the mass of the keg be m1 and that of the beer be m2. Total mass M = m1+ m2.

Various forces acting on the beer keg are shown in the fig.. Total weight Mg is resolved into components Mgcosθ perpendicular to the ramp and Mgsinθ parallel to the ramp. Normal reaction N = Mgcosθ. F is the frictional force on the keg surface from the ramp.

Net linear force acting on the keg parallel to the ramp = Mgsinθ -F. Under this net force the keg starts to accelerate linearly down the ramp. In other words, this net force provides the keg with linear acceleration (and velocity) parallel to the ramp.

Linear acceleration of the keg down the ramp = a = (Mgsinθ ...

#### Solution Summary

This solution is comprised of a detailed explanation to use synthetic division to find the quotient q(x) and remainder r.

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