Math_Alegebra

Math Study guide chapter 9, 12, and 11 Chapter 9 Section 1-Prime factorization -Prime number is a whole number, greater then 1, whose only factors are 1 and itself Examples- 2,3,5,7,11,13,17 -Composite numbers is a whole number greater than 1, that has more than two factors Examples- 4, 6, 8, 10, 12, 14, 15, 16, 18 90 = 2 x 45 2 x 2 x 15 2 x 3 x 3 x 5 Section 2- factoring 12a² + 16a = 2a (6a) + 2a (8) 2a (6a + 8) Section 3- factoring F.O.I.L = First, outside, inside, and last X² + 7x + 12 (x+4)(x+3) Section 4- factoring 5x² + 27x + 10 (x+5)(5x+2) 4x² + 24x+ 32 4(x² + 6x +8) 4(x+4)(x+2) Section 5, 6- the four special cases (x+y)² = x² + 2xy + y² = (x+y)(x+y) (x-y)² = (x-y)(x-y)= x² - 2xy+ y² (x-y)(x+y) = x² - y² Prime = x² + y² Chapter 12 Section 2- simplify radial expressions 15 = 5 12 4 X² -2x-15 = (x+3)(x-5) = x-5 X²-x-12 (x+3)(x-4) x-4 When you have variables in the denominators, you must make sure the denominator in not 0. These are the excluded values. 2x-10 x² -25 = (x-5)(x+5) excluded values are 5 and -5 Section 3- multiplying national expressions To multiply rational numbers expressed as fractions, you multiply numerators and multiply denominators. You can use this same method to multiply rational expressions. When you multiply fraction that involve units of measure, you can divide by the units in the same way that you divide by variables Section 4- dividing rational expressions Recall that to divide rational numbers expressed as fractions you multiply by the reciprocal of the divisor. You can use this same method to divide rational expressions. 5x² ÷ 10x³ = 5x² • 21 7 21 7 10x³ Section 7- rational expressions with unlike denominators Least common multiple (LCM) is the least number that is a common multiple of two or more numbers. Denominators: 12bc² + 32 b²c= 96b³c³ Section 8- mixed expressions and complex expressions Changing mixed expressions to rational expressions is similar to changing mixed numbers to improper fractions. For a problem 3 + 6 x+3 The LCD (least common denominator) Add the numbers Distributive property And simplify Section 9- solving rational equations For 12 + 4 X+5 (x+2) Cross multiply Distributive property Add -4x and -24 to each side Then divide Chapter 11- Radical and Rational Functions Section 1- simplifying radical expressions (√a•b) = √a • √b; √4•7 = √4 •√7 = 2√7 No radicands can have a per square factor except 1 No radicand can be left as a fraction No radicals can be in the denominator √20=√5•4=2√5 3√10 • 4√10= 12√10•10= 120 √(54a²b²)= 3ab√6 Section 2- adding and subtraction radical expressions 4√3 + 7√3 = 11√3 Radical expressions in which the radicands are alike can be added or subtracted in the same way that monomials are added or subtracted. 7√3 + 4√3 = 3√3 Section 3- solving radical equations Get √ on the side by itself Square both sides to get rid of √ Solve the equation You must check your solutions in the original problem to see if they work you may have extraneous roots Section 4- Pythagorean Theorem a^2+b^2=c^2 In a right triangle, the side opposite the right angle is called the hypotenuse. This side is always the longest side of a right triangle. The other two sides are called the legs of the triangle. In a right triangle where a+b is legs + c is the hypotenuse. To determine if a triangle is a right triangle a²+b²=c² Section 5- distance formula D²=(x-x)² + (y-y)² Section 6- similar triangles If two shapes are similar, one is an enlargement of the other. This means that the two shapes will have the same angles and their sides will be in the same proportion (e.g. the sides of one triangle will all be 3 times the sides of the other etc.). angle A = angle D angle B = angle E angle C = angle F AB/DE = BC/EF = AC/DF = perimeter of ABC/ perimeter of DEF Two triangles are similar if: 1) 3 angles of 1 triangle are the same as 3 angles of the other or 2) 3 pairs of corresponding sides are in the same ratio or 3) An angle of 1 triangle is the same as the angle of the other triangle and the sides containing these angles are in the same ratio. Section 7- trigonometric functions Sin = opposite/hypotenuse Cos = adjacent/ hypotenuse Tan = opposite/ adjacent