Chapter 15

Solve the given problems. If \(f(x)=3 x^{3}-5 a x^{2}-3 a^{2} x+5 a^{3},\) find \(f(x) \div(x+a)\)

Solve the given problems. In finding the electric current in a certain circuit, it is necessary to factor the denominator of \(\frac{2 s}{s^{3}+5 s^{2}+4 s+20} \cdot\) Is (a) \((s-2)\) or (b) \((s+5)\) a factor?

Solve the given problems. In the theory of the motion of a sphere moving through a fluid, the function \(f(r)=4 r^{3}-3 a r^{2}-a^{3}\) is used. Is \((\text { a) } r=a\) or (b) \(r=2 a\) a zero of \(f(r) ?\)

Solve the given problems. In finding the volume \(V\) (in \(\mathrm{cm}^{3}\) ) of a certain gas in equilibrium with a liquid, it is necessary to solve the equation \(V^{3}-6 V^{2}+12 V=8\) Use synthetic division to determine if \(V=2 \mathrm{cm}^{3}\)

Solve the given problems. In finding the volume \(V\) (in \(\mathrm{cm}^{3}\) ) of a certain gas in equilibrium with a liquid, it is necessary to solve the equation \(V^{3}-6 V^{2}+12 V=8\) Use synthetic division to determine if \(V=2 \mathrm{cm}^{3}\)