**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.

As per Bartleby guidelines, for more than one questions asked, only first is to be answered. Please…

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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

**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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