Solving Polynomial Equations n r a e l

Solving Polynomial Equations n r a e l l l ’ u o ty a h W To solve polynomials equations by factoring. To solve polynomials equations by graphing. Use graphing technology to find approximate solutions for polynomial equations. Use polynomials equations to solve real world problems. y r a l u Vocab Sum of the cubes= Difference of the cubes=

Remember: If is a factor of polynomial, then the polynomial has a value 0 when x=a. If a is a real number, then the graph of the polynomial has (a, 0), as an x-intercept. When you have a polynomial factoring that polynomial will help you to solve the equation like So to solve a polynomial equation by factoring Write the equation in the form P(x)=0 Factor P(x). Use the Zero Property of the roots

Problem 1: Solving Polynomial Equation Using Factors. What are the real or imaginary solutions of each polynomial equations? Make equation=0 and get GCF Make equation =0, Divide by 3 and get GCF Factor Use quadratic to solve Zero property and solve for x

Your turn What are the real or imaginary solutions of each equation? Answers:

Take a note

Problem 2: Solving Polynomial Equations by Factoring What are the real or imaginary solutions of each polynomial equation? A. Make the equation =0 Let then Factor with -4 and +1 Replace back Then and Two imaginary roots

Verify your answer with the graphic calculator The graphs shows zero at x=2, and x=-2. it also shows three turning points. This means that are imaginary roots, which do not appear on the graph

Problem 2 What are the real or imaginary solutions of each polynomial equation? B. Make equation =0 The three solutions are

Your turn What are the real or imaginary solutions of each polynomial equations? Answer: c) Answer: a) Answer b)

Problem 3: Finding Real Roots by Graphing What are the real solutions of the equation Method 1: graph Use the intersect feature to find the x values of the points of intersection. Approximate solutions are x=-1. 09, x=1. 16, and x=3. 93

Method 2: Rewrite the equation as Graph the related function. Use the zero feature The solutions are the same that in method 1, so the approximate solutions are x=-1. 09, x=1. 16, and x=3. 93 Verify the solutions by showing that they satisfy the original equation. Show values of in a table.

Your turn: a)What are the real solutions of the equation. b)Which method seems to be easier and more reliable way to find the solutions of an equations? Explain Answer a) -1. 84 b) the second method seems to be a more reliable way to find the solutions because you do not risk missing a point of intersection

Problem 4: Modeling a real world situation Close friends Stacy, Una, and Amir were all born on July 4. Stacy is one year younger than Una is two years younger than Amir. On July 4, 2010, the product of their ages was 2300 more than the sum of their ages. How old was each friend on that day? Answer Let x=Una’s age on July 4, 2010 Stacy’s age=x-1 Amir’s age=x+2 Sum of their ages x+(x-1)+(x+2)+2300 = Product of their ages x(x-1)(x+2) Graph it and look into the tabl when y=0 and take only the solution that makes sense x=13. Una was 13, Stacy 12 and Amir 15

Your turn A. What are three consecutive integers whose product is 480 more than their sum. Answer: 7, 8, 9 Input the data in the function feature and look for the table when y=0. B. What are three consecutive even integers whose product is 4 times their sum? Answer: 2, 4, 6 or -6, -4, -2

Classwork odd Homework even TB pgs 301 exercises 1 -56