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Magazine Problem 2
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 \(\mathbb{R}\). \(-4+3 i\) degree 2
Problem 3
Express the statement as a formula that involves the given variables and a constant of proportionality \(k,\) and then determine the value of \(k\) from the given conditions. \(V\) varies directly as the cube of \(r .\) If \(r=3,\) then \(V=36 \pi\)
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
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 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 \(\mathbb{R}\). \(2,-2-5 i\) degree 3
Problem 4
Find the quotient and remainder if \(f(x)\) is divided by \(p(x)\). $$f(x)=3 x^{3}-5 x^{2}-4 x-8 ; \quad p(x)=2 x^{2}+x$$
Problem 4
Express the statement as a formula that involves the given variables and a constant of proportionality \(k,\) and then determine the value of \(k\) from the given conditions. \(S\) is directly proportional to the square of \(x .\) If \(x=2,\) then \(S=24\)
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
Sketch the graph of \(f\) for the indicated value of \(c\) or \(a\). \(f(x)=a x^{3}-3\) (a) \(a=-2\) (b) \(a=\frac{1}{8}\)
