amt Algebra 1 Skills Needed to be Successful in Algebra 2 E. Factoring F. Radicals

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1 amt Algebra 1 Skills Needed to be Successful in Algebra 2 A. Simplifying Polynomial Expressions Apply the appropriate arithmetic operations and algebraic properties needed to simplify an algebraic expression. Simplify polynomial expressions using addition and subtraction. Multiply a monomial and polynomial. B. Solving Equations Solve multi-step equations. Solve a literal equation for a specific variable, and use formulas to solve problems. C. Rules of Exponents Simplify expressions using the laws of exponents. Evaluate powers that have zero or negative exponents. D. Binomial Multiplication Multiply two binomials. E. Factoring Identify the greatest common factor of the terms of a polynomial expression. Express a polynomial as a product of a monomial and a polynomial. Find all factors of the quadratic expression ax + bx + c by factoring and graphing. F. Radicals Simplify radical expressions. G. Graphing Lines Identify and calculate the slope of a line. Graph linear equations using a variety of methods. Determine the equation of a line. H. Regression and Use of the Graphing Calculator Draw a scatter plot, find the line of best fit, and use it to make predictions. Graph and interpret real-world situations using linear models.

A. Simplifying Polynomial Expressions I. Combining Like Terms You can add or subtract terms that are considered "like", or terms that have the same variable(s) with the same exponent(s). Ex. 1: 5x - 7y + IOx + 3y 15x - 4y lox + u Ex.

2 A. Simplifying Polynomial Expressions I. Combining Like Terms You can add or subtract terms that are considered "like", or terms that have the same variable(s) with the same exponent(s). Ex. 1: 5x - 7y + IOx + 3y 15x - 4y lox + u Ex. 2: -8h h h h 3 Il. Applying the Distributive Property Every term inside the parentheses is multiplied by the term outside of the parentheses. Ex. 1: Ex. 2: 4x2 (5x3 + 6x) 3-9x x-12 4x 2 5x3 + 4x 2 6x 20x x 3 Ill. Combining Like Terms AND the Distributive Property (Problems with a Mix!) Sometimes problems will require you to distribute AND combine like terms!! 3 4x x 12x-6+ Ex. 2: 36x x 25x-6 54x

PRACTICE SET 1 Simplify. l. 8x 9Y+ 12y 16x -1-3 3. 5n (3 4n) 2. 14Y+22-15y 2 +23y 16 4. -20 lb -3) 5.

3 PRACTICE SET 1 Simplify. l. 8x 9Y+ 12y 16x n (3 4n) 2. 14Y+22-15y 2 +23y lb -3) 5. IOq(16x+11) IIO 6. (5x 6) 7. 3(18z 4w) + 2(10z 6w) 8. (8c +3) +12(4c -10) '71-1-L w (y -x) + 7) 6

I. Solving Two-Step Equations A couple of hints: Ex. 1: 41-2=30 B. Solving Equations l. To solve an equation, UNDO the order of operations and work in the reverse order. 2. REMEMBER!

4 I. Solving Two-Step Equations A couple of hints: Ex. 1: 41-2=30 B. Solving Equations l. To solve an equation, UNDO the order of operations and work in the reverse order. 2. REMEMBER! Addition is "undone" by subtraction, and vice versa. Multiplication is "undone" by division, and vice versa. 4x = Ex.2: 87=-11x = l Ix 11 *-11 Il. Solving Multi-step Equations With Variables on Both Sides of the Equal Sign When solving equations with variables on both sides of the equal sign, be sure to get all terms with variables on one side and all the terms without variables on the other side. Ex. 3: 8x+4= 4x x 4x X = 24 Ill. Solving Equations that need to be simplified first In some equations, you will need to combine like terms and/or use the distributive property to simplify each side of the equation, and then begin to solve it. Ex. 4: 8X X 20x-35=10X+45 -lox -lox lox-35= lox =

PRACTICE SET 2 Solve each equation. You must show all work. 1. 5x-2=33 35 5 5 3. 8(3x a) = 196 I o QC 4x + 36 10 x 4. 45x 720 + 15x = 60 & 31 5. 4(12x - 9.5 60 60 x z 13 6.

5 PRACTICE SET 2 Solve each equation. You must show all work. 1. 5x-2= (3x a) = 196 I o QC 4x x 4. 45x x = 60 & (12x x z = k 131= Ill = -2(3x - 82) x =18+3x 10 3X to IV. 9.5 Solving Literal Equations x A literal equation is an equation that contains more than one variable. You can solve a literal equation for one of the variables by getting that variable by itself (isolating the specified variable). Ex. l: 3xy = 18, 3xy 18 3y 3y 6 Solve for x. Ex.2: 5a-10b= 20, Solve for a. +10b = + 10b 5a = b 20 10b a = 4 +2b 8

6 PRACTICE SET 3 Solve each equation for the specified variable. 1. Y+V=W, for V = 81, for w 3. 2d-3f= 9, forf q )180, forg 4. dx+t 10, for x -z lo-t u, for x -7+5 k Ito 9

C. Rules of Exponents Multiplication: Recall (x m (m+n) 4 Ex: (3x y2 ) = Division: Recall x x (m n) Ex: 42m5J2 3m3j 42 3.2 = 14m j.

7 C. Rules of Exponents Multiplication: Recall (x m (m+n) 4 Ex: (3x y2 ) = Division: Recall x x (m n) Ex: 42m5J2 3m3j = 14m j.1 ) 2 Powers: Recall (xm y = x (m n) Ex: ( 2a 3 bc 43 ) = b 3 c 12 ) (c ) = 8a Power of Zero: Recall xo = 1, x 0 Ex: 5x o y4 = = 5y4 PRACTICE SET 4 Simplify each expression. c 8 c m 3 m j'3z10 5y3z 7. (-t 7 ) f3go 9. 3 GO a4b6 36ab 2 c 3 C ll. (3m2n)4 12. (12x 2 y) LIX 10

I. Reviewing the Distributive Property D. Binomial Multiplication The distributive property is used when you want to multiply a single term by an expression. Ex 1: 8(5x 9x) 8 5x + 8 ( 9x) 401-721 Il.

8 I. Reviewing the Distributive Property D. Binomial Multiplication The distributive property is used when you want to multiply a single term by an expression. Ex 1: 8(5x 9x) 8 5x + 8 ( 9x) Il. Multiplying Binomials the FOIL method When multiplying two binomials (an expression with two terms), we use the "FOIL" method. The "FOIL" method uses the distributive property twice! FOIL is the order in which you will multiply your terms. First Outer Inner Last Ex. 1: (x + 10) FIRST OUTER First 2 (X ) Outer Inner x 10 -> 10x > 6x INNER LAST Last 6 10 x2 + lox + 6x+ 60 > 60 x2 + 16x+ 60 (After combining like terms) 11

9 Recall : 42 =4-4 x Ex. (x+ Now you can use the "FOIL" method to get a simplified expression. PRACTICE SET 5 Multiply. Write your answer in simplest form. 2. ( + ) x 12) X + x OtO X 5x-8k X l ox + to 5. ( - l)ßx+ ) x-4)gx+ ) 6. (- + Ux+5) lox hox +50 I tx 100* +50 X (_x + 5)2ee ( 10. (2x-3) 2 x X lox 12

3/28/2017 Hou to Factor Polynomials Easily CnAnr Home Pre Algebra Help Free Algebra Help Free Geometry Help Trigonometry Free Worksheets Free Calculators Math Help Blog Free Teaching Tools Math

10 3/28/2017 Hou to Factor Polynomials Easily CnAnr Home Pre Algebra Help Free Algebra Help Free Geometry Help Trigonometry Free Worksheets Free Calculators Math Help Blog Free Teaching Tools Math People Cool Math Games How to Factor Rules of Fractions Math Search Engine Advertising How to Factor Polynomials Learning how to factor polynomials does not have to be difficult. GradeA will break down the steps for you, show you simple examples with visual illstrations, and also give you some clever tips and tricks. Use the followina steps to factor your polynomials: 1) Take out the GCF if possible * Learn how to factor out a GCF 2) Identify the number of terms More information about terms * 2 term factorinq techniques * 3 term factoring techniques 3) Check by multiplying Check with Math FOIL system Do you want to know how to solve quadratic equations (ex: x2 + 8x+ 15 = 0)? Learn how to solve quadratic equations, which is a different type of problem than factoring, so it requires a different process. Factoring Binomials: The Differece of Two Squares Remember, make sure to always factor out a GCE first. Sometimes that's the only part of the binomial that can be factored. Once you have checked for the GCF, then you can move forward to solving the problem: If you are taking a basic algebra class, you probably only need to know one type of factoring when you have two terms: its called the difference of two squares. You need to know how to factor the difference of two squares if you want to know how to factor polynomials. Stay connected Like 331 RSS 2 x2 is a "square" because it = x is a "square" because it = 4-4 square #1 minus square #2 The example shown above is very common factoring problem. It is called the difference of two squares because it is a subtraction problem ("difference" indicates subtraction) and they are perfect squares between there is some number times itself that gives you that number. MQr.g-a.ÄQUt-EEf-e-C,t-S.AUa.C-eS. Here are a few more examples of difference of two squares: x2-25 4x2 49 9x2-36 Now, onto the factoring.. S.tep_l: Find the square root of each term. Ste.2_2. Factor into two binomials - one plus and one minus. http J/ n/how-to-factor-pdynomids.html 1/3

Northwood High School Algebra 2/Honors Algebra 2 Summer Review Packet

Northwood High School Algebra 2/Honors Algebra 2 Summer Review Packet This assignment should serve as a review of the Algebra 1 skills necessary for success. Our hope is that this review will keep your