Adding and Subtracting Rational Expressions

7.3 - Special Factoring

Difference of Squares:
x^2 - y^2 = (x + y) (x - y)
Perfect Square:
x^2 +2xy + y^2 = (x + y)^2
x^2 - 2xy + y^2 = (x - y)^2
Difference of Cubes:
x^3 - y^3 = (x + y)(x^2 + xy + y^2)
Sum of Cubes:
x^3 + y^3 = (x + y)(x^2 -xy +y^2)

7.1 , 7.2

7.1
Ex 1: Factor out greatest common factor.
1. 10x - 30
= 10(x+3)
Ex 2: Factor by grouping.
1. 2k + 2h + jk + jh
=2(k + h) j(k+h)
= (k + h)(2 + j)
7.2
EX 1: Factor the trinomial.
1. y^2 + 7y -30
= (y - 3) (y + 10)
EX 2:
1. 7p^2 +15pq +2q^2)
= (7p + ?) (p + ?)
= (7p + q) (p + 2q)

Remember Chapter 8!!!

So we also did an intro to functions in Chapter 8.

This includesRational Expressions and Functions: Multiplying and Dividing

And Adding and Subtracting Rational Expressions

For functions remember that f(x)=y and g(x)=y

How to pronounce: "f of x" of "g of x"

Final Review!

This is what we have learned this term in math!

Chapter 6: Exponents, Polynomials, and Polynomial Functions

6.1- Integer Exponents and Scientific Notation

6.2-Adding and Subtracting Polynomials

6.3-Polynomial Functions

6.4-Multiplying Polynomials

6.5 Dividing Polynomials

Chapter 7: Factoring

7.1-Greatest Common Factors; Factoring by Grouping

7.2-Factoring Trinomials

7.3-Special Factoring

7.4-Solving Equations by Factoring

Chapter 12: Nonlinear Functions, Conic Sections, and Nonlinear Systems

12.1-Additional Graphs and Logarithmic Functions

Chapter 11: Exponential and Logarithmic Functions

11.1-Inverse Functions

Chapter 10: Quadratic Functions, Inequalities, and Functions

10.1-The Square Root Property and Completing the Square

10.2-The Quadratic Formula

10.3-Equations in Quadratic Form

Square root Propery

If x and k are complex numbers and x^2 = k, then

x = SQRT k or x = -SQRT K

non quadratic function

A non quadratic function can be written like this: au^2 + bu + c = 0