1. Warm Up
1. Divide f(a) = 4a2 – 3a + 6 by a – 2 using any method.
Now find f(2).
List any similarities. Why do you think this occurs?

2. Remainder and Factor Theorem
6-7
Remainder and Factor Theorem
SWBAT
use the remainder to find the remainder of dividing polynomials.
use the factor theorem to factor polynomials
Holt McDougal Algebra 2
Holt Algebra 2

3. Recall that if a number is divided by any of its factors, the remainder is 0. Likewise, if a polynomial is divided by any of its factors, the remainder is 0.
The Remainder Theorem states
if a polynomial is divided by (x – a)
the remainder is the value of the function at a.

4. Find the remainder of: f(x) = 3x3 – 2x2 + x – 11 and x – 3

5. Factor Theorem: If the remainder of your equation = 0
Then x – a is a factor of the quotient
You have to use Synthetic or Long Division
f(x) = x4 + x3 – 17x2 – 20x + 32 and x – 4
(x – 4) (x3 + 5x2 + 3x – 8)

6. Determine whether the given binomial is a factor of the polynomial P(x).
A. (x + 1); (x2 – 3x + 1)
Find P(–1) by synthetic substitution.
P(–1) = 5
P(–1) ≠ 0, so (x + 1) is not a factor of P(x)
B. (x + 2); (3x4 + 6x3 – 5x – 10)
Find P(–2) by synthetic substitution.
P(–2) = 0, so (x + 2) is a factor of P(x)

7. Factor Theorem Show that x + 3 is a factor of
f(x) = x3 + 6x2 – x – 30. Then solve for x.
(x+3)(x – 2)(x + 5), so x = -3, 2, -5

8. Try on your own. Pg #2

9. Homework: Page 359
#10-22 Even
Bring in book tomorrow

10. Warm Up – do not share books/ipads
PG 360
# 43

11. Remainder and Factor Theorem
6-7
Remainder and Factor Theorem
SWBAT
use the remainder to find the remainder of dividing polynomials.
use the factor theorem to factor polynomials
Holt McDougal Algebra 2
Holt Algebra 2

12. Factor Theorem
Use the graph of the polynomial. To factor the x3 – 3x2 – 6x + 8 completely.

13. PARCC Example
Answer: W: x – 4 L: x + 8 H: x – 1 Try on your own: pg 359 # 3

14. Real World Example (use calc)
Pg 359 #3-5

15. Use synthetic division.
PARCC Question
Write an expression that represents the area of the top face of a rectangular prism when the height is x + 2 and the volume of the prism is x3 – x2 – 6x.
The volume V is related to the area A and the height h by the equation V = A  h. Rearranging for A gives A = . V h
x3 – x2 – 6x
x + 2
A(x) =
Substitute.
Use synthetic division.
The area of the face of the rectangular prism can be represented by A(x)= x2 – 3x.

16. PARCC Example
Write an expression for the length of a rectangle with width y – 9 and area y2 – 14y + 45.
The area A is related to the width w and the length l by the equation A = l  w.
y2 – 14y + 45
y – 9
l(x) =
Substitute.
Use synthetic division.
The length of the rectangle can be represented by l(x)= y – 5.

17. Did We Reach Our Objective?
Use the factor theorem.
Use the remainder theorem.

18. HOMEWORK
Pg 360
# 29 – 33 all