I am a problem solver Not a problem makerI am an answer giver not an answer takerI can do problems I haven’t seenI know that strict doesn’t equal meanIn this room we do our bestTaking notes -practice –quiz- testThe more I try the better I feelMy favorite teacher is Mr. Meal…..ey

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

Pascal’s Triangle and the Binomial Theorem

(x + y)0 = 1

(x + y)1 = 1x + 1y

(x + y)2 = 1x2 + 2xy + 1y2

(x + y)3 = 1x3 + 3x2y + 3xy2 +1 y3

(x + y)4 = 1x4 + 4x3y + 6x2y2 + 4xy3 + 1y4

(x + y)5 = 1x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + 1y5

(x + y)6 = 1x6 + 6x5y1 + 15x4y2 + 20x3y3 + 15x2y4 + 6xy5 + 1y6

7.5.2

Expand the following.

a) (3x + 2)4

= 4C0(3x)4(2)0 + 4C1(3x)3(2)1 + 4C2(3x)2(2)2 + 4C3(3x)1(2)3 + 4C4(3x)0(2)4

n = 4a = 3x b = 2

= 1(81x4) + 4(27x3)(2) + 6(9x2)(4) + 4(3x)(8) + 1(16)

= 81x4 + 216x3 + 216x2 + 96x +16

b) (2x - 3y)4

= 4C0(2x)4(-3y)0 + 4C3(2x)1(-3y)3

= 1(16x4)

= 16x4 - 96x3y + 216x2y2 - 216xy3 + 81y4

n = 4a = 2x b = -3y

7.5.6

Binomial Expansion - Practice

+ 4C1(2x)3(-3y)1 + 4C2(2x)2(-3y)2 + 4C4(2x)0(-3y)4

+ 4(8x3)(-3y) + 6(4x2)(9y2) + 4(2x)(-27y3) + 81y4

Match these up

You have a room with an area of and an area rug with an area of . What is the area of the floor that is not covered by the rug?

You have a cylinder whose top has an area of and a height. What is the volume of the cylinder?

You know that the length of a room is of a foot longer than twice your height in feet and the width of the room is 6 feet longer than half your height plus your dog’s height. Write an expression for the width and the length of the room in terms of your heights. Then find the area

Write a negative polynomial function with roots . Sketch a possible graph

Write a positive polynomial function with roots 3.Sketch a possible graph

Create a negative odd polynomial function and sketch the graph

Simplifying

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

Examples:

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.

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)