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Section 5.3 : Graphing Polynomials

Sketch the graph of each of the following polynomials.

1. \(f\left( x \right) = - {x^3} - {x^2} + 17x - 15 = - \left( {x - 1} \right)\left( {x - 3} \right)\left( {x + 5} \right)\)
2. \(A\left( x \right) = {x^3} + 2{x^2} - 3x\)
3. \(h\left( x \right) = {x^4} + 2{x^3} - 3{x^2}\)
4. \(g\left( x \right) = {x^4} + 14{x^3} + 68{x^2} + 136x + 96 = {\left( {x + 2} \right)^2}\left( {x + 4} \right)\left( {x + 6} \right)\)
5. \(Q\left( x \right) = - {x^5} + 8{x^4} - 13{x^3} - 22{x^2} + 32x + 32 = - {\left( {x - 4} \right)^2}{\left( {x + 1} \right)^2}\left( {x - 2} \right)\)
6. \(P\left( x \right) = - {x^4} + 5{x^3} - 6{x^2} - 4x + 8 = - {\left( {x - 2} \right)^3}\left( {x + 1} \right)\)
7. \(h\left( x \right) = {x^5} + 5{x^4} - 18{x^3} - 58{x^2} + 145x - 75 = {\left( {x - 1} \right)^2}{\left( {x + 5} \right)^2}\left( {x - 3} \right)\)
8. \(R\left( x \right) = {x^6} - 2{x^5} - 11{x^4} + 12{x^3} + 36{x^2} = {x^2}{\left( {x + 2} \right)^2}{\left( {x - 3} \right)^2}\)