Chapter 9 Review

1. Chapter 9 Review

2. 9-1 Adding & Subtracting Polynomials • Monomials – one term • Binomials – two terms • Trinomials – three terms • Polynomials – more than three terms • The degree of a monomial is the sum of the exponents of the variables, a constant have a degree of zero • Standard form of a polynomial means that the degree of its monomials terms decrease from left to right • When you are adding/subtracting polynomials you can only add/subtract like terms • You can only add/subtract the coefficients not the variables exponents • Remember when you subtract to change the signs of the second expression to their opposite then add • Practice problems Page 497 1-38all, 43-48all, 53, 54

3. 9-2 Multiplying & Factoring • When you multiply a monomial by a polynomial, distribute it into the parenthesis so that you get rid of the parenthesis • Remember that when you multiply variables you add the exponents • When you are looking for the Greatest Common Factor (GCF) if you need to do the factor tree then do one. If the terms have variables attached, make sure that you take the lowest exponent from the variable that they all have • If you are factoring out a monomial out of an expression, ask yourself “ What do I have to multiply my GCF by to get my first term, then the second and so on” • Practice problems Page 501 1-24all, 27-32all, 34-39all

4. 9-3 Multiplying Binomials • When you are multiplying binomials use FOIL First Outer Inner Last • Make sure you combine like terms • In general, if you start with 4 terms you will end with 3 term, a trinomial • If you start with a binomial and a trinomial (5 terms) you will end with 4 terms • I recommend that you write this types of problems out vertically so that you line up like terms. It makes getting mixed up a lot less likely. • Practice problems Page 507 1-19all,22-38all

5. 9-4 Multiplying Special Cases • If you have something that is “squared” write it down twice and FOIL it like you would any other problem. There is a formula that is available but that is just one more thing for you to memorize. • If you have to parenthesis that exactly the same exempt that one has an addition sign and the other has a subtraction sign, then square the first term and square the second term and put a subtraction sign in between the two terms. • Practice problems Page 515 1-8all, 15-20all, 28-39all, 44-52all

6. 9-5 Factoring Trinomials of the Type x² + bx + c • Follow the rules that I gave you during class. If you went to Holy Spirit or Norte Dame than make sure you write that on the top of your test, otherwise, you must show me all your work like I showed you • Make sure that if the three terms have something in common, a number and/or a variable factor it out prior to factoring the trinomial. I will mark it down if it is not factored completely. • Practice problems Page 521 5-16all, 21-29all, 33-38all, 43-54all

7. 9-6 Factoring Trinomials of the Type ax² + bx + c • You do the same way you did the ones in 9-5 however this time you cannot take the shortcut to check your answers. • Again, make sure you factor out anything the expression may have in common prior to making your “x” • Practice problems Page 525 1-27all, 33-41all, 44-46all

8. 9-7 Factoring Special Cases • The only special cases that you have are the ones that only have two terms. If both terms are perfect squares then take the square roots of each, write each down twice, put an addition sign in one parenthesis and a subtract sign in the other parenthesis. • If neither one is a perfect square then check to see if they are both divisible by a number they will make them both perfect squares. • Don’t forget to include that number and/or variable in you final answer. • If you have the same parenthesis twice, write it as once as a squared • Practice problems Page 531 1-6all, 10-36all, 45-53all, 56-64all