1. I am a problem solver Not a problem maker I am an answer giver not an answer taker I can do problems I haven’t seen I know that strict doesn’t equal mean In this room we do our best Taking notes -practice –quiz- test The more I try the better I feel My favorite teacher is Mr. Meal…..ey

2. CONSTRUCTING THE TRIANGLE 1 ROW 0 1 1 ROW 1 1 2 1 ROW 2 1 3 3 1 ROW 3 1 4 6 4 1 R0W 4 1 5 10 10 5 1 ROW 5 1 6 15 20 15 6 1 ROW 6 1 7 21 35 35 21 7 1 ROW 7 1 8 28 56 70 56 28 8 1 ROW 8 1 9 36 84 126 126 84 36 9 1 ROW 9 2

3. Pascal’s Triangle and the Binomial Theorem (x + y) 0 = 1 (x + y) 1 = 1x + 1y (x + y) 2 = 1x 2 + 2xy + 1y 2 (x + y) 3 = 1x 3 + 3x 2 y + 3xy 2 +1 y 3 (x + y) 4 = 1x 4 + 4x 3 y + 6x 2 y 2 + 4xy 3 + 1y 4 (x + y) 5 = 1x 5 + 5x 4 y + 10x 3 y 2 + 10x 2 y 3 + 5xy 4 + 1y 5 (x + y) 6 = 1x 6 + 6x 5 y 1 + 15x 4 y 2 + 20x 3 y 3 + 15x 2 y 4 + 6xy 5 + 1y 6 7.5.2

4. Expand the following. a) (3x + 2) 4 = 4 C 0 (3x) 4 (2) 0 + 4 C 1 (3x) 3 (2) 1 + 4 C 2 (3x) 2 (2) 2 + 4 C 3 (3x) 1 (2) 3 + 4 C 4 (3x) 0 (2) 4 n = 4 a = 3x b = 2 = 1(81x 4 )+ 4(27x 3 )(2)+ 6(9x 2 )(4)+ 4(3x)(8) + 1(16) = 81x 4 + 216x 3 + 216x 2 + 96x +16 b) (2x - 3y) 4 = 4 C 0 (2x) 4 (-3y) 0 + 4 C 3 (2x) 1 (-3y) 3 = 1(16x 4 ) = 16x 4 - 96x 3 y + 216x 2 y 2 - 216xy 3 + 81y 4 n = 4 a = 2x b = -3y 7.5.6 Binomial Expansion - Practice + 4 C 1 (2x) 3 (-3y) 1 + 4 C 2 (2x) 2 (-3y) 2 + 4 C 4 (2x) 0 (-3y) 4 + 4(8x 3 )(-3y)+ 6(4x 2 )(9y 2 )+ 4(2x)(-27y 3 )+ 81y 4

6. Match these up

8. Create a negative odd polynomial function and sketch the graph

9. Simplifying A rational expression is simplified or reduced to lowest terms when the numerator and denominator have no common factors other than 1. Examples:

11. Simplifying Rational Expressions 1.Factor both the numerator and denominator as completely as possible. 2.Divide out any factors common to both the numerator and denominator.

12. Factoring a Negative 1 Remember that when –1 is factored from a polynomial, the sign of each term in the polynomial changes. Example: – 2x + 5 = – 1(2x – 5) = –(2x – 5)