1. Unit 3 - Day 5 Polynomial Long Division
Objective:
SWBAT determine if (x-c) is a factor of a polynomial, through long division, and the factor theorem.

2. Simplify the following: 3(x2 + 8x) - 2(2x2 - 6x - 9) ½(3x - 1)(2x - 3)
Warm Up
Simplify the following:
3(x2 + 8x) - 2(2x2 - 6x - 9)
½(3x - 1)(2x - 3)
Use long division to divide 548 by 3.
For #2, write out the solution as a division statement to relate to p(x) / d(x) = q(x) + r(x)/d(x)
And as a product statement to relate to q(x) * d(x) +r(x) = p(x)

3. So we can add, subtract, and multiply polynomials together
So we can add, subtract, and multiply polynomials together...what about divide?
(3x3 + 4x2 - 2x - 1)
÷ =
(x + 4)

4. x + 4
3x3 + 4x2 - 2x - 1
Demonstrate right next to the numerical example.
Point out the similarities

5. You try: (1-a) Polynomial Division ~worksheet~

6. p(x) ÷ d(x) = q(x) + r(x)/d(x)
p(x) = q(x) × d(x) + r(x)
Relate back to numerical example in warm up

7. When we divide p(x) by (x - c), the remainder r(x) is equal to p(c).
Remainder Theorem:
When we divide p(x) by (x - c), the remainder r(x) is equal to p(c).
Relate back to numerical example from warm up

8. When p(c) = 0, then (x - c) is a factor of the polynomial p(x).
Factor Theorem:
When p(c) = 0, then (x - c) is a factor of the polynomial p(x).
Relate back to numerical example from warm up

9. You try: (1-b) Is (x-2) a factor of the polynomial?
Apply factor/remainder theorem. Find P(2)!!!

10. Is there an easier way to divide polynomials?
Yes, it’s called Synthetic Division

11. (3x3 + 4x2 - 2x - 1)
÷ =
(x + 4) -4
Note that this only works with factors in the form of (x-c) or (ax-c)
Relate to long division

12. (2x4 - 3x2 +4)
÷ =
(x - 2) 2
Example with coefficients of zero

13. Classwork: Polynomial Division ~worksheet~
HW:
Finish worksheet