Work through the You Try It Exercise: Solve Linear Equations in One Variable showing all steps below.

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1 Section 5.4 Guided Notebook Section 5.4 Polynomial Equations and Models A. BEFORE beginning Section 5.4, complete homework Chapter 5 Sec 1-3 Review of Factoring. Read the ebook and watch section videos (5.1, 5.2 & 5.3) as needed. B. Fill in the Guided Notes below for the following objectives: Work through Section 5.4 TTK #1 on page Work through Section 5.4 TTK #2 on page Work through Section 5.4 TTK #3 on page Work through Section 5.4 TTK #4 on page Work through Objective 1 then complete homework Obj Work through Objective 2 then complete homework Obj Work through Objective 3 then complete homework Obj Work through the You Try It Exercise: Solve Linear Equations in One Variable showing all steps below. Work through the You Try It Exercise: Use Linear Equations to Solve Application Problems showing all steps below 213

2 Work through the You Try It Exercise: Express Equations of Functions Using Function Notation showing all steps below Work through the You Try It Exercise: Factor Polynomials Completely showing all steps below 214

3 Section 5.4 Objective 1: Solve Polynomial Equations by Factoring What is a polynomial equation? When is a polynomial equation in standard form? What is the degree of a polynomial equation? What is the zero product property? Watch the video on and write down the two examples that are explained in the video. 215

4 Work through Example 1 showing all steps below. Solve (x + 3)(x 7) = 0 Summarize the Caution statement on and give another example. What are the steps to solve polynomial equations by factoring? Work through Example 2 showing all steps below. For part b, click on the link to check your answer. If your answers are incorrect, watch the accompanying video to find your error. 216

5 Solve each equation by factoring. a. y 2 + 2y 15 = 0 b. z 3 + z 2 = z + 1 Work through Example 3 showing all steps below. For part b, click on the link to check your answer. If your answers are incorrect, watch the accompanying interactive video to find your error. Solve each equation by factoring. a. (x + 2)(x + 5) = 18 b. (x + 3)(3x 5) = 5(x + 1)

6 Work through Example 4 showing all steps below. For part b, click on the link to check your answer. If your answers are incorrect, watch the accompanying interactive video to find your error. Solve each equation by factoring. a k 10 k b. 0.02x x = Work through Example 5 showing all steps below. Click on the link to check your answer. If your answers are incorrect, watch the accompanying interactive video to find your error. Solve the equations by factoring. a. 4x 2 = 64x b. 4x x 2 = 2x 15 c. h 3 + h 2 = -6h 218

7 If P(x) is prime, does this mean the polynomial equation P(x) = 0 has no solutions? Why or why not? Now complete homework Obj Section 5.4 Objective 2: Find the Zeros of a Polynomial Function What is a zero or root of a function? Write the definition of the zero of a function. 219

8 Graphically the zeros are the same as the of the graph. Explain why. Work through Example 6 showing all steps below. Find the zeros for each polynomial function using its graph. Draw each graph. What are the zeros of a polynomial function? 220

9 Watch the animation on and take notes below. Work through Example 7 showing all steps below. For parts c d, click on the link to check your answer. If your answers are incorrect, watch the accompanying interactive video to find your error. Find the zeros for each polynomial function. a. g(x) = 12x 3 8x 2 32x b hx ( ) x 3x 221

10 c. f(x) = 3x 2 24x + 48 d. p(x) = x 3 + 2x 2 9x 18 Summarize the relationship between the zeros, x-intercepts and factors of a simplified polynomial function and a real number c. 222

11 Now complete homework Obj Section 5.4 Objective 3: Use Polynomial Equations and Models to Solve Application Problems Summarize the Caution statement on using your own words. What is the feasible domain? 223

12 Work through Example 8 showing all steps below. The Burj Dubai, the world s tallest building at 2683 feet, has an observation deck on the 124 th floor. An object is thrown upward with an initial velocity of 16 feet per second off the edge of the observation deck. The height of the object h, in feet, after t seconds is given by the function h(t) = -16t t How long will it take for the object to hit the ground? What is the Pythagorean Theorem and when can it be used? When using the variables a, b and c what side of the triangle must c represent? 224

13 Watch the video with Example 9 and answer the questions below. Zip line rides are popular activities at many vacation destinations. A zip line consists of a pulley mounted on a cable and set at an incline. The zip line uses gravity to propel a rider from one end to the other. For one such ride the length of the zip line is 30 feet shorter than seven times the rise of the lines. The run of the line is 30 feet longer than six times the rise of the line. Find the length of the zip line. 1. Draw the diagram of the situation 2. Why did he choose x to be the rise of the zip line? 3. Explain the expression 7x Explain the expression 6x What is used to relate the sides? 6. What is the equation for the problem? 225

14 7. Show all the steps to solve the equation. 8. Answer the question in the problem. Watch the video with Example 10 and answer the questions below. A club wants to remodel its rectangular stage area to make room for seating on three sides. The stage measures 10 meters by 20 meters. The width of the seating area is the same on all three sides and the total combined area of the stage and seating area is 648 square meters. Find the width of the seating area x. 1. Draw the diagram of the situation. 2. How is x defined? 3. What is the formula for the area of a rectangle? 226

15 4. What is an expression for the length? Explain it. 5. What is an expression for the width? Explain it. 6. What is the equation that represents the problem? 7. Show all steps to solve the equation. 8. Answer the question in the problem. Now complete homework Obj NOTE: There is no online or written test for Chapter 5. Questions from this chapter will be included on later exams. 227

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