ANGLE BISECTOR
ANGLE BISECTOR BEING COPIED
Step 1: Draw an arc that is centered at the vertex
of the angle. This arc can have a radius of any length.
However, it must intersect both sides of the angle.
We will call these intersection points P and Q
This p
The factorial function is defined as:
F(n) = n(n - 1)(n - 2)(n - 3) . (2)(1)
where n is a non-negative integer.
We define F(0) = 1 and F(1) = 1 .
The factorial function F(n) is also represented as " n! ", read " n factorial."
Examples.
5!
=
5(4)(3)(2)(1)
nother way to represent data is in a matrix. An mn matrix has m rows and n columns, and each entry is
given a unique name, based on its row and column:
A=
The matrix A is often denoted [A] .
The number of rows and the number of columns are called dimensio
An expression of the form a 3 - b 3 is called a difference of cubes. The factored form of a 3 - b 3 is (a - b)
(a 2 + ab + b 2) :
(a - b)(a 2 + ab + b 2) = a 3 - a 2 b + a 2 b - ab 2 + ab 2 - b 3 = a 3 - b 3
For example, the factored form of 27x 3 - 8 ( a
When we discuss a rational expression in this chapter, we are referring to an expression whose
numerator and denominator are (or can be written as) polynomials. For example, and are rational
expressions.
Writing a Rational Expression in Lowest Terms
To wr
When we discuss a rational expression in this chapter, we are referring to an expression whose
numerator and denominator are (or can be written as) polynomials. For example, and are rational
expressions.
Writing a Rational Expression in Lowest Terms
To wr
We can factor a difference of fourth powers (and higher powers) by treating each term as the square of
another base, using the power to a power rule. For example, to factor x 4 - y 4 , we treat x 4 as (x 2)2 and
y 4 as (y 2)2 . Thus, x 4 - y 4 = (x 2)2 -
To solve a rational equation, such as +1 - = , rewrite all the terms of the equation as fractions with a
common denominator. For example, +1 - = can be rewritten as:
+1 - =
+ - =
Next, eliminate the denominator:
4x 2 - x + x 2 - x - 3 = x 2 + 5x - 6
Sol
To add or subtract rational expressions with like denominators, add or subtract their numerators and
write the result over the denominator. Then, simplify and factor the numerator, and write the expression
in lowest terms. This is similar to adding two fr
Here is the expansion of (x + y)n for n = 0, 1, 5 :
(x + y)0 = 1
(x + y)1 = x + y
(x + y)2 = x 2 +2xy + y 2
(x + y)3 = x 3 +3x 2 y + 3xy 2 + y 3
(x + y)4 = x 4 +4x 3 y + 6x 2 y 2 +4xy 3 + y 4
(x + y)5 = x 5 +5x 4 y + 10x 3 y 2 +10x 2 y 3 +5xy 4 + y 5
Look
Pascal's Triangle is a triangle in which each row has one more entry than the preceding row, each row
begins and ends with "1," and the interior elements are found by adding the adjacent elements in the
preceding row. The triangle is symmetrical.
Figure %