1. Splash Screen

2. Mathematical Practices 7 Look for and make use of structure.
Content Standards
A.APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
F.IF.7.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Mathematical Practices
7 Look for and make use of structure.
CCSS

3. Evaluate functions by using synthetic substitution.
You used the Distributive Property and factoring to simplify algebraic expressions.
Evaluate functions by using synthetic substitution.
Determine whether a binomial is a factor of a polynomial by using synthetic substitution.
Then/Now

4. Synthetic Substitution
If f(x) = 2x4 – 5x2 + 8x – 7, find f(6).
Use synthetic/long division to solve
(2x4 – 5x2 + 8x – 7) (x-6).
Example 1

5. Concept

6. If f(x) = 2x3 – 3x2 + 7, find f(3).
A. 20
B. 34
C. 88
D. 142
Example 1

7. Find Function Values
COLLEGE The number of college students from the United States who study abroad can be modeled by the function S(x) = 0.02x 4 – 0.52x x x , where x is the number of years since 1993 and S(x) is the number of students in thousands. How many U.S. college students will study abroad in 2011?
Answer: In 2011, there will be about 451,760 U.S. college students studying abroad.
Example 2

8. Warm Up When is divided by (x+5), a student can determine the remainder by evaluating f(r).
a.) What is the value of r?
b.) Evaluate f(r).

9. Intro Question If (x+6) divides p(x) evenly, which statement must be true?
a.) -6 is the slope of p(x)
b.) p(-6)=0
c.) 6 is the y-intercept of p(x)
d.) p(6)=0

10. Concept

11. Use the Factor Theorem
Determine whether x – 4 is a factor of 2x3 + 7x2 – 53x – 28. Then find the remaining factors of the polynomial.
Example 3

12. Group Practice: Collaboration Time!
Show that x-3 is a factor of Then find the remaining factors of the polynomial.
Show that x+2 is a factor of
Then find the remaining factors of the polynomial.

13. End of the Lesson