1. Name:__________ warm-up 5-6
Factor the polynomial x 3 – 800. If the polynomial cannot be factored, write prime
Factor the polynomial 64x 5 + 8x 2y 3. If the polynomial cannot be factored, write prime
Factor the polynomial x 5 + 8y 3. If the polynomial cannot be factored, write prime
Factor the polynomial 24x³ -24. If the polynomial cannot be factored, write prime

2. If the area of a parallelogram is given by x2 – 6x + 5 and the base is x – 1, what is the height of the figure?
The volume of a box is given by the expression x3 - 5x2 + 8x – 4. The height of the box is given by the expression x – 1. Find an expression for the area of the base of the box.

3. 5-6 The Remainder and Factor Theorem
x 6 – 35x = 0.
x 4 – 29x = 0.
x 4 – 29x = 0

4. Details of the Day Activities: EQ:
How do polynomials functions model real world problems and their solutions?
I will be able to…
Activities:
Warm-up
Review homework
Notes:
Marking Period Exam – November 13
All make-up work due Wednesday, -no Nov 2 exceptions
Vocabulary:
synthetic substitution
depressed polynomial
Evaluate functions by using synthetic substitution.
. Determine whether a binomial is a factor of a polynomial by using synthetic substitution. .

5. A Quick Review
Factor 8c3 – g3. If the polynomial is not factorable, write prime.
Factor 12az – 6bz – 6cz + 10ax – 5bx – 5cx. If the polynomial is not factorable, write prime.
Factor 8x3m2 – 8x3n2 + y3m2 – y3n2. If the polynomial is not factorable, write prime.
Solve 16d4 – 48d = 0.

6. A Quick Review Solve k3 + 64 = 0.
The width of a box is 3 feet less than the length. The height is 4 feet less than the length. The volume of the box is 36 cubic feet. Find the length of the box.

7. Notes and examples If f(x) = 2x4 – 5x2 + 8x – 7, find f(6).
Synthetic Substitution
2 Direct Substitution

8. Notes and examples
If f(x) = 2x3 – 3x2 + 7, find f(3).

9. Notes and examples
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?
HIGH SCHOOL The number of high school students in the United States who hosted foreign exchange students can be modeled by the function F(x) = 0.02x 4 – 0.05x x 2 – 0.02x, where x is the number of years since 1999 and F(x) is the number of students in thousands. How many U.S. students will host foreign exchange students in 2013?

10. Notes and examples
Since the remainder is 0, (x – 3) is a factor of the polynomial. The polynomial x3 + 4x2 – 15x –18 can be factored as (x – 3)(x2 + 7x + 6). The polynomial x2 + 7x + 6 is the depressed polynomial. Check to see if this polynomial can be factored.
Determine whether x – 3 is a factor of x3 + 4x2 – 15x – 18. Then find the remaining factors of the polynomial.
x2 + 7x + 6 = (x + 6)(x + 1) Factor the trinomial
You can see that the graph of the related function f(x) = x3 + 4x2 – 15x – 18 crosses the x-axis at 3, –6, and –1. Thus, f(x) = (x – 3)[x – (–6)][x – (–1)]. 

11. Notes and examples
Determine whether x + 2 is a factor of x3 + 8x2 + 17x If so, find the remaining factors of the polynomial.

12. Notes and examples

13. Notes and examples