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

Ways to solve quadratic equations

1. Factor--zero factor property
2. Square root property
3. Completing the square, difficult to factor trinomial

Remember

You cannot distribute an exponent over addition and subtraction.

Quadratic formula reminder

This is a great way to make sure that your know how to use the quadratic formula


http://www.youtube.com/watch?v=s80J2dAUUyI

Page 634

In class today, JoJo told us about page 634, a summary of all the importnat points gone over in 10.1-10.3. It's helpful because it gives you a quick rundown of all the important info that will be on our test tomorrow.
Good luck on your test!
Brigid

Important things to remember for the test

The Discriminant
If a, b and c are integers then the discriminant, b^2-4ac of ax^2+bx+c=0 determines the number and type of solutions as follows.
If the descriminate is posivtive the square of an integer then the number of solutions is two rational solutions.
If the discriminate is positive not the square of an integer then the numer of solutions is two irrational solutions
If the descriminate is zero then the number of solutions is one rational solution.
If the discriminate is negativwe then the number of solutions is two nonreal complex solutions.

10.3 Review

Here is a review problem from 10.3

x^4+x^2-12=0
(x^2)2 u=x^2
u^2+u-12
(u+4)(u-3)
u=-4 and u=3
x^2=-4 and x^2=3
x= SQRT-4 and x=SQRT3
x=2i and x=SQRT3

Test Review 10.1-10.3

Something that I found in the book that I think is helpful to go over for the test is on page 589 in our books. On the page there is a chart and it states all of the different methods for solving quadratic equations and each methods advantages and disadvantages. I think this is really helpful because it tells you when you should use which method and which method would be easiest to use when solving a certain equation! On the same page there are also some review problems that are helpful!

10.3 Equations in Quadratic Form Examples

Ex1:
X^4-13x^2+36=0
(x^2)^2-=363x^2+36=0 => u=x^2
u^2-13u+36=0
(u-9)(u-4)
UX^2=9 or x^2=4
x=+/-3 or x=+/-2
x= 3,-3,2,-2
Ex2:
2(4m-3)^2+7(4m-3)+5=0
4m-3=p=>2p^2+7p+5=0
(2p+5)(p+1)=0
p=-5/2 or p=-1
4m-3=5/2 or 4m-3=-1
4m= -5/2+3
4m=1/2
m=1/8
m=1/2
m= 1/8,1/2
m=1/8