Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Notes for Chapter 5 Factoring GCF (Greatest Common Factor) For as set of monomials find: 1. the common coefficients 2. the common variables 3. place these common parts outside parenthesis 4. divide each monomial by the common parts, placing the results inside the parenthesis Example: 48 x 6 y 2 40 x 4 y 3 becomes 8 x 4 y 2 (6 x 2 5 y) Trinomial factoring (leading coefficient of 1, x 2 bx c ) Find 2 factors of ‘c’ whose sum is ‘b’ Calculator help c y1 In the tables, find ‘b’ in y 2 . Read the factors in the remaining columns. x y 2 x y1 Example: x 2 7 x 12 in factored form becomes (x+3)(x+4). Trinomial factoring (leading coefficient ‘a’ not 1, ax 2 bx c ) Find 2 factors of ‘a’ times ‘c’ whose sum is ‘b’ Calculator help ac y1 In the tables, find ‘b’ in y 2 . Read the factors in the remaining columns. x y 2 x y1 GCF GCF GCF ax fx 2 GCF fx c ‘f’ is for either factor of ‘ac’. Find the horizontal and vertical GCF, to find the factors. Make the GCF negative, if the box next to it is negative. Example: 12 x 2 7 x 10 12*(-10) = -120 Factors of 120 that add to -7 are 8 and -15. 3x 4x -5 2 2 12x -15x 8x -10 Result: (4x-5)(3x+2) Special case factoring – Difference of Squares a2 b2 becomes (a b)( a b) Example: x 2 64 becomes Note that 8*8=64 (a perfect square) ( x 8)( x 8) Special case factoring – Sum of Cubes a3 b3 becomes (a b)( a 2 ab b 2 ) Example: x 3 64 becomes ( x 4)( x 2 4 x 16) Note that 4*4*4-64 (a perfect cube) Special case factoring – Difference of Cubes a3 b3 becomes (a b)( a 2 ab b 2 ) Example: x 3 64 becomes Note that 4*4*4-64 (a perfect cube) ( x 4)( x 2 4 x 16) Multiplying binomials FOIL method (First, Outside, Inside Last) Synthetic Division – divisor coefficient of 1 Example: x 3 2 x 2 5x 6 x3 -3] 1 2 -5 -6 ____ -3_ 3 6 1 -1 -2 Result: x 2 x 2 2nd Example (missing elements of the polynomial) x 3 125 x5 -5] 1 0 0 125 ____ -5_ 25 -125 1 -5 25 Result: x 2 5 x 25 Synthetic Division – divisor coefficient not 1 Example: 2 x 3 x 2 5x 2 2x 1 Divide everything by the coefficient of the divisor - (2 in this example) x3 1 | 2 1 2 5 x x 1 2 2 1 x 2 1 5 -1 2 2 1 1 1 2 2 ________________ 1 -1 -2 1 Result: x 2 x 2 Complex numbers i 1 i 2 1 i 3 i Know the powers of i. i4 1 Complex number convention; i is not in the denominator. Multiply by the conjugate to remove the imaginary number from the denominator. 3i multiply by the conjugate to simplify this fraction. 1 2i 3 i 1 2i 3 6i i 2 5 5i * 1 i 1 2i 1 2i 1 2i 2i 4 5 Using the calculator, set mode to a+bi . Also, use FRAC to decipher results. Solving equations in one variable Use inverse operations appropriately: Operation Addition Subtraction Multiplication Division Squaring Cubing Inverse Operation Subtraction Addition Division Multiplication Square Root Cube Root Example: 5 2 x 3 12 2 x3 7 7 2 49 x3 4 49 49 12 x 3 4 4 4 61 x 15.25 4 x3 Be prepared to use multiple skills to solve any individual problem presented.