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Algebra 1 Skills Needed to Be Successful in Algebra 2

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Algebra 1 Skills Needed to Be Successful in Algebra 2 amt Algebra 1 Skills Needed to be Successful in Algebra 2 A. Simplifying Polynomial Expressions Objectives: The student will be able to: 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 Objectives: The student will be able to: Solve multi-step equations. Solve a literal equation for a specific variable, and use formulas to solve problems. C. Rules of Exponents Objectives: The student will be able to: Simplify expressions using the laws of exponents. Evaluate powers that have zero or negative exponents. D. Binomial Multiplication Objectives: The student will be able to: Multiply two binomials. E. Factoring Objectives: The student will be able to: 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 Objectives: The student will be able to: Simplify radical expressions. G. Graphing Lines Objectives: The student will be able to: 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 Objectives: The student will be able to: 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 lox + u 15x - 4y 3 Ex. 2: -8h2 + 10h3 - 12112 - 15h 3 3 -20112 - 5h Il. Applying the Distributive Property Every term inside the parentheses is multiplied by the term outside of the parentheses. Ex. 1: Ex. 2: 4x2(5x 3 + 6x) 3-9x-3•4 4x 2 • 5x3 + 4x 2 • 6x 3 27x-12 20x 5 + 24x Ill. Combining Like Terms AND the Distributive Property (Problems with a Mix!) Sometimes problems will require you to distribute AND combine like terms!! Ex.2: 3•4x-3-2+13x 12x-6+ 36x-15+63-90x 25x-6 —54 x + 48 5 PRACTICE SET 1 Simplify. l. 8x—9Y+ 12y 2. 14Y+22-15y 2 +23y 16x -1-3 — 16 3. 5n—(3 —4n) 4. -20 lb -3) 5. IOq(16x+11) 6. —(5x —6) IIO 7. 3(18z — 4w) + 2(10z —6w) 8. (8c +3) +12(4c -10) '71-1-L w 60 10. -(y -x) + 7) 6 B. Solving Equations I. Solving Two-Step Equations A couple of hints: 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. Ex.1: 41-2=30 Ex.2: 87=-11x+21 -21 -21 4x = 32 66 = —lIx +4 +4 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 + 28 —4 —4 8x 4x + 24 4X = 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 + 45 + 2X 20x-35=10X+45 -lox -lox lox-35=45 +35 +35 lox = 80 +10 +10 7 PRACTICE SET 2 Solve each equation. You must show all work. 1. 5x-2=33 4x + 36 QC 35 I o 5 5 10 x 3. 8(3x —a) = 196 4. 45x—720 + 15x = 60 &31 9.5 60 60 x z 13 5. 4(12x - 6. 198=154+71-68 -—15k x 131= 8. -71-10=18+3x 10 —131 1 —3X —90 -Ill — 10 —to 9. 121 +8 - 15 = -2(3x - 82) 10. 9.5 x IV. Solving Literal Equations 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.2: 5a-10b= 20, Solve for a. Ex. l: 3xy = 18, Solve for x. +10b = + 10b 3xy 18 5a = 20 +10b 3y —3y 20 10b 6 5 5 5 a = 4 +2b 8 PRACTICE SET 3 Solve each equation for the specified variable. 1. Y+V=W, for V = 81, for w 3. 2d-3f= 9, forf 4. dx+t— 10, for x __q+34 -zlo-t 201-9 5. )180, forg 6. —1 + u, for x -7+5k Ito 9 C. Rules of Exponents m (m+n) Multiplication: Recall (x Ex: (3x 4y2 ) = x .2 (m—n) 42m5J2 42 2 Division: Recall Ex: ) .1 = —14mj x —3m3j —3 (m•n) 1343 9 3 Powers: Recall (xmy = x Ex: (—2a3bc 43 ) = ) (c ) = —8ab c12 Power of Zero: Recall xo = 1, x 0 Ex: 5xoy4 = = 5y4 PRACTICE SET 4 Simplify each expression. 1.105 m 15 2. 3. m 3 c c8 45j'3z10 5. 6. 5y3z 3 7. (-t 7) 8. 3f3go 9. 3 GO 12a4b6 10. ll. (3m2n)4 12. (12x 2 y) 0 36ab2c 3 C 13. 14. 15. LIX 10 D. Binomial Multiplication I. Reviewing the Distributive Property 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. 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) OUTER First 2 FIRST Outer x•10 -> 10x (X+ + 10) Inner > 6x Last 6•10 > 60 INNER LAST x2 + lox + 6x+ 60 x2 + 16x+ 60 (After combining like terms) 11 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 —lox + to 5. ( - l)ßx+ ) 6. (- + Ux+5) + -- 53—3 —lox—hox+50 Itx —100*+50 7. x-4)Gx+ ) X 100 9. (_x+ 5)2ee ( 10. (2x-3) 2 x 1 — +2-5 X —lox 12 3/28/2017 Hou to Factor Polynomials Easily CnAnr Stay connected How to Factor Polynomials Like 331 Learning how to factor polynomials does not have to be difficult. GradeA will RSS Home break down the steps for you, show you simple examples with visual illstrations, Pre Algebra Help and also give you some clever tips and tricks. Free Algebra Help Use the followina steps to factor your polynomials: Free Geometry Help 1) Take out the GCF if possible Trigonometry out a GCF Free Worksheets * Learn how to factor Free Calculators 2) Identify the number of terms Math Help Blog More information about terms Free Teaching Tools * 2 term factorinq techniques Math People * 3 term factoring techniques Cool Math Games 3) Check by multiplying How to Factor Check with Math FOIL system Rules of Fractions Math Search Engine Do you want to know how to solve quadratic equations (ex: x2 + 8x+ 15 = 0)? Advertising 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. 2 x2 is a "square"because it = x — 16 16 is a "square"because it = 4-4 square #1 minus square #2 The example shown above is very commonfactoring 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/www.gradeamatNElp.ca•n/how-to-factor-pdynomids.html 1/3.
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