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Find a degree 
Magazine Problem 2
Find a polynomial \(f(x)\) of degree 3 that has the indicated zeros and satisfies the given condition. $$-5,2,4 ; \quad f(3)=-24$$
Problem 3
A polynomial \(f(x)\) with real coefficients and leading coefficient 1 has the given zero(s) and degree. Express \(f(x)\) as a product of linear and quadratic polynomials with real coefficients that are irreducible over \(\mathbb{R}\). $$2,-2-5 i; \quad \text { degree } 3$$
Problem 3
Exer. 1-12: Express the statement as a formula that involves the given variables and a constant of proportionallty \(k,\) and then determine the value of \(k\) from the given conditions. \(r\) varies directly as \(s\) and inversely as \(t .\) If \(s=-2\) and \(t=4\) then \(r=7\)
Problem 3
Find a polynomial \(f(x)\) of degree 3 that has the indicated zeros and satisfies the given condition. $$-4,3,0 ; \quad f(2)=-36$$
Problem 3
Find the quotient and remainder if \(f(x)\) is divided by \(p(x)\). $$f(x)=3 x^{3}+2 x-4 ; \quad p(x)=2 x^{2}+1$$
Problem 3
Identify any vertical asymptotes, horizontal asymptotes, and holes. $$f(x)=\frac{-2(x+5)(x-6)}{(x-3)(x-6)}$$
Problem 3
Sketch the graph of \(f\) for the indicated value of \(c\) or \(a\) $$f(x)=a x^{3}+2$$ (a) \(a=2\) b) \(a=-\frac{1}{3}\)
Problem 4
Find a polynomial \(f(x)\) of degree 3 that has the indicated zeros and satisfies the given condition. $$-3,-2,0 ; \quad f(-4)=16$$
Problem 4
Identify any vertical asymptotes, horizontal asymptotes, and holes. $$f(x)=\frac{2(x+4)(x+2)}{5(x+2)(x-1)}$$
Problem 4
Sketch the graph of \(f\) for the indicated value of \(c\) or \(a\) $$f(x)=a x^{3}-3$$ (a) \(a=-2\) b) \(a=\frac{1}{4}\)
