91Ó°ÊÓ

Use the rational zeros theorem to completely factor \(P(x)\) into linear factors. (Hint: Not all zeros of \(P(x)\) are rational. $$P(x)=21 x^{4}+13 x^{3}-103 x^{2}-65 x-10$$

For each polynomial at least one zero is given. Find all others analytically. $$P(x)=-x^{3}+4 x^{2}+7 x-28 ; 4$$

Determine a window that will provide a comprehensive graph of each polynomial function. ( In each case, there are many possible such windows. $$P(x)=-5.9 x^{3}+16 x^{2}-120$$

Use the rational zeros theorem to completely factor \(P(x)\) into linear factors. (Hint: Not all zeros of \(P(x)\) are rational. $$P(x)=2 x^{4}+7 x^{3}-9 x^{2}-49 x-35$$

Solve each problem. Give approximations of linear measures to the nearest hundredth. Buoyancy of a Spherical Object It has been determined that a spherical object of radius 4 inches with specific gravity 0.25 will sink in water to a depth of \(x\) inches, where \(x\) is the least positive root of the equation $$x^{3}-12 x^{2}+64=0$$ To what depth will this object sink if \(x<10 ?\)

Use the given zero to completely factor \(P(x)\) into linear factors. Zero: \(i ; \quad P(x)=x^{5}-x^{4}+5 x^{3}-5 x^{2}+4 x-4\)

Factor \(P(x)\) into linear factors given that \(k\) is a zero of \(P\). $$P(x)=2 x^{3}-3 x^{2}-17 x+30 ; \quad k=2$$

Use the given zero to completely factor \(P(x)\) into linear factors. Zero: \(-3 i ; \quad P(x)=x^{5}+2 x^{4}+10 x^{3}+20 x^{2}+9 x+18\)

Factor \(P(x)\) into linear factors given that \(k\) is a zero of \(P\). $$P(x)=2 x^{3}-3 x^{2}-5 x+6 ; \quad k=1$$

Determine a window that will provide a comprehensive graph of each polynomial function. ( In each case, there are many possible such windows. $$P(x)=2 \pi x^{4}-12 x^{2}+100$$