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Show your answers clearly and neatly! For problems #4 and #5, write the polynomial function as a product of linear factors (in factored form). 4. k(x) = x5 – 9x³ Factored form: k(x) = Degree Zeros Multiplicity Crosses/Touches Sign End behavior

Show your answers clearly and neatly! For problems #4 and #5, write the polynomial function as a product of linear factors (in factored form). 4. k(x) = x5 – 9x³ Factored form: k(x) = Degree Zeros Multiplicity Crosses/Touches Sign End behavior

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Educational Website Content** Show your answers clearly and neatly! For problems #4 and #5, write the polynomial function as a product of linear factors (in factored form). **4.** \( k(x) = x^5 - 9x^3 \) - **Factored Form:** \( k(x) = \) | Degree | Zeros | Multiplicity | Crosses/Touches | |--------|-------|--------------|-----------------| | | | | | **Graph:** A blank Cartesian plane is provided for sketching the graph of the polynomial. --- **5.** \( m(x) = -x^5 - 3x^4 \) - **Factored Form:** \( m(x) = \) | Degree | Zeros | Multiplicity | Crosses/Touches | |--------|-------|--------------|-----------------| | | | | | **Graph:** A blank Cartesian plane is provided for sketching the graph of the polynomial. --- **6.** For the graph, determine whether the degree is odd or even and whether the leading coefficient is positive or negative. (*Circle the correct response.*) **Graph Analysis:** A graph with a curve crossing the y-axis and changing concavity multiple times is shown. - **Degree:** Even or Odd - **Leading Coefficient:** \( a < 0 \) or \( a > 0 \) Select the correct options based on the behavior of the graph shown.
Transcribed Image Text:**Educational Website Content** Show your answers clearly and neatly! For problems #4 and #5, write the polynomial function as a product of linear factors (in factored form). **4.** \( k(x) = x^5 - 9x^3 \) - **Factored Form:** \( k(x) = \) | Degree | Zeros | Multiplicity | Crosses/Touches | |--------|-------|--------------|-----------------| | | | | | **Graph:** A blank Cartesian plane is provided for sketching the graph of the polynomial. --- **5.** \( m(x) = -x^5 - 3x^4 \) - **Factored Form:** \( m(x) = \) | Degree | Zeros | Multiplicity | Crosses/Touches | |--------|-------|--------------|-----------------| | | | | | **Graph:** A blank Cartesian plane is provided for sketching the graph of the polynomial. --- **6.** For the graph, determine whether the degree is odd or even and whether the leading coefficient is positive or negative. (*Circle the correct response.*) **Graph Analysis:** A graph with a curve crossing the y-axis and changing concavity multiple times is shown. - **Degree:** Even or Odd - **Leading Coefficient:** \( a < 0 \) or \( a > 0 \) Select the correct options based on the behavior of the graph shown.
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