1. Solving Polynomial Equations
What you’ll learn
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.
Vocabulary
Sum of the cubes=
Difference of the cubes=

2. 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

3. 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

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

5. Take a note

6. 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

7. 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

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

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

10. 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

11. 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.

12. 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

13. 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. 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?
Let x=Una’s age on July 4,2010
Stacy’s age=x-1
Amir’s age=x+2
Answer
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 table,
when y=0 and take only the
solution that makes sense
x=13. Una was 13,Stacy 12
and Amir 15

14. A. What are three consecutive integers whose product
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

15. Classwork odd Homework even
TB pgs 301 exercises 1-56