Cubic Functions Quiz Review ANSWERS

U4 L1-L5 Review Sheet: Cubic Equations Find all the rational zeros of (f(x)=6x^{3}+11x^{2}-3x-2) \[\{-2,-1/3,2\})\] Write a polynomial function of least degree that has the given zeros: 4, 1, 5, \[y=x^{3}-2x^{2}-19x+20\] Find all the zeros of (f(x)=x^{3}+6x^{2}+21x+26) \[\{-2,-2\pm3i\}\] Given a polynomial and one of its factors, find the other factors: (x^{3}+2x^{2}-x-2;x-1) \[\{-2,-1,1\})\] Find all the rational roots of: (f(x)=x^{3}-6x^{2}+10x-8) \[\{4, 1\pm i\}\) a) Describe the left behavior of: (f(x)=-x^{5}+3:) xi-00 b) Describe the right behavior of \(f(x)=x^{4}+3x^{2}+1:\) 00 f(x) 00 odd left decreases when a even right increases when \[a=\#\] Find all the zeros of (f(x)=x^{3}-7x^{2}+25x-175) \[\{\pm5i,7\}\] For which part of the domain is the graph (f(x)=x^{3}-6x^{2}+3x+10) positive? ((-1,2)\cup(5,\infty)) For which part of the domain is the graph of (f(x)=x^{3}-5x^{2}+2x-1) negative? ((-\infty,4.61)) Write a polynomial function of least degree that has the given roots: (4,-2\pm\sqrt{3}) \[y=x^{3}-15x-4\]