1. Absolute Value Problems  Why do we create two problems when solving an absolute value problem?  Let's first return to the original definition of absolute value:absolute value  "| x | is the distance of x from zero."  For instance, since both –2 and 2 are two units from zero, we have | –2 | = | 2 | = 2:  Since there are two answers to every abs problem there must be two equations to solve for both answers!

2. Absolute Value Inequalities Stephan’s question: Why do we flip the sign for the negative part of the equation?

3. Absolute Value Inequalities "| x | is the distance of x from zero." For the inequality: | x | < 3. All the points between –3 and 3, but not actually including– 3 or 3, will work in this inequality. For the inequality: | x | > 2. The solution will be all points that are more than two units away from zero. For instance, since both –2 and 2 are two units from zero, we have | –2 | = | 2 | = 2:

4. Multiplying Polynomials  FOIL is the same as distributing  A*A = A 2 but A + A = 2A  Exponent Rules:  A2* A3 = A5  (A2)3 = A6

5. Factoring  ALWAYS LOOK FOR GCF FIRST!!!!  Difference of 2 perfect squares  Trinomial factoring

6. Factoring By Grouping  Multiply the coefficient of A by C  Find two numbers that multiply to this new number and add to B  Break the trinomial into two binomials, using these two factors  Factor the GCF out of each binomial  Re-group the factors

7. Rational Expressions Chapter 2  In order to add/subtract fractions denominators must match exactly  When multiplying…do top*top and bottom*bottom

8. Complex Rational Expressions  First add the two terms in the top  Then add the terms in the bottom  Then flip 2 nd fraction and multiply  reduce

9. Rational Equations  Always remember the difference between an EXPRESSION and an EQUATION… for expressions denominators do NOT cancel away  For equations… make all denominators equal and then remove them from the equation

10. Rational Inequalities  You MUST make a number line to solve inequalities with variables in the denominator  Find what number makes the denominator undefined…add it to the #line  Solve the inequality…add answer to the number line  Choose a # between the 2 #’s on the #line and shade in if the number works in the original equation and shade out if it doesn’t

11. Chapter 3- Radicals  A square root in the calc is ^(1/2)  A cube root in the calc is ^(1/3)  A nth root in the calc is ^(1/n)  You cannot have negative numbers under the radical sign if the index (small #) is even 

12. Multiplying and Dividing  You can multiply and divide any numbers or variables as long as the indexes are the same  √a*√b = √a*b  √(a/b) = √a /√b

13. Adding/Subtracting and Simplifying Radicals  You can only add/subtract radicals that have the same index, variables, exponents and numbers under the radical sign  To simplify a number under a radical sign re-write it as multiplication of its factors…pick factors that are perfect squares/ cubes/ etc.

14. Simplifying Variables in Radicals  For square roots divide even exponents by 2 and move outside the radical  For square roots with odd exponents divide by 2 and leave remainder under the radical  For cubes or any root higher divide by the index and leave the remainder under the radical

15. Rationalizing Denominators  Never leave a radical in a denominator  Multiply monomials by the radical divided by the radical  Multiply binomials by the conjugate

16. Radical Equations  Isolate the radical  Square both sides of the equation  Solve and check answer  If there is more than one radical… separate so that each is on its own side of the equation, then repeat the first 3 steps until all radical are gone  CHECK ANSWERS