logging in or signing up COLLEGE ALGEBRA 2 livycat Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 855 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: May 06, 2009 This Presentation is Public Favorites: 1 Presentation Description No description available. Comments Posting comment... By: rpriya (31 month(s) ago) Hi, can i get the copy of the ppt please. Saving..... Post Reply Close By: livycat (31 month(s) ago) I NEED YOUR E-MAIL ADDRESS. KINDLY POST IT HERE. Saving..... Edit Comment Close Premium member Presentation Transcript Slide 1: ALGEBRA Engr. Lizette Ivy G. Catadman Instructor / Lecturer LECTURE NOTES & PROBLEM SETS: PART 2 Slide 2: TYPE PRODUCTS SUM AND DIFFERENCE OF TWO TERMS (BINOMIALS) SQUARE OF A BINOMIAL Slide 3: TYPE PRODUCTS PRODUCT OF TWO BINOMIALS CASE 1 PRODUCT OF TWO BINOMIALS CASE 2 Slide 4: TYPE PRODUCTS CUBE OF A BINOMIAL SQUARE OF A TRINOMIAL Slide 5: TYPE PRODUCTS SQUARE OF A MULTINOMIAL PRODUCT OF A BINOMIAL AND A TRINOMIAL Slide 6: TYPE PRODUCTS BINOMIAL RAISED TO POWER n Slide 7: TYPE PRODUCTS BINOMIAL RAISED TO POWER n PASCAL’S TRIANGLE Slide 8: FACTOR TYPES COMMON FACTOR DIFFERENCE OF TWO SQUARES Slide 9: FACTOR TYPES PERFECT TRINOMIAL SQUARE SUM AND DIFFERENCE OF TWO CUBES Slide 10: FACTOR TYPES TRINOMIALS WITH DISTINCT FACTORS THE TRINOMIAL MUST BE ARRANGED IN DESCENDING POWERS OF THE GIVEN VARIABLE. IN THE ABOVE EQUATIONS, IT IS THE VARIABLE x. Slide 11: FACTOR TYPES TRINOMIALS WITH DISTINCT FACTORS IF THE LAST SIGN IN THE TRINOMIAL IS (+), THE SIGNS IN THE BINOMIAL FACTORS ARE THE SAME. IF THE MIDDLE TERM OF THE TRINOMIAL IS (+), THE SIGNS IN BOTH BINOMIALS ARE (+). IF THE MIDDLE TERM OF THE TRINOMIAL IS (-), THE SIGNS IN BOTH BINOMIALS ARE (-). Slide 12: FACTOR TYPES TRINOMIALS WITH DISTINCT FACTORS IF THE LAST SIGN IN THE TRINOMIAL IS (-), THE SIGNS IN THE BINOMIALS ARE DIFFERENT. TAKE THE PRODUCT OF THE INNER TERMS AND OUTER TERMS OF THE FACTORS (BINOMIALS). WHICHEVER HAVE THE HIGHER RESULT WILL CARRY THE SIGN OF THE MIDDLE TERM OF THE TRINOMIAL. Slide 13: MORE COMPLICATED FACTOR TYPES FACTORING BY REARRANGEMENT AND GROUPING CASE 1: IF A POLYNOMIAL HAS FOUR TERMS, IT MAY BE FACTORED OUT BY FIRST, SEPARATING IT INTO TWO GROUPS AND FACTORING EACH GROUP SEPARATELY. IF EACH OF THE TWO GROUPS HAS A COMMON FACTOR, THEN THE POLYNOMIAL CAN BE FACTORED OUT. Slide 14: MORE COMPLICATED FACTOR TYPES FACTORING BY REARRANGEMENT AND GROUPING CASE 2: IF A POLYNOMIAL HAS FOUR TERMS, SEPARATE THREE TERMS THAT WILL FORM A TRINOMIAL PERFECT SQUARE. IF THE EVENTUAL RESULT IS IN THE FORM OF THE DIFFERENCE OF TWO SQUARES, THE POLYNOMIAL CAN BE FACTORED OUT. Slide 15: MORE COMPLICATED FACTOR TYPES FACTORING BY REARRANGEMENT AND GROUPING CASE 1: CASE 2: Slide 16: MORE COMPLICATED FACTOR TYPES SUM AND DIFFERENCE OF TWO ODD POWERS DIFFERENCE OF TWO EVEN POWERS Slide 17: MORE COMPLICATED FACTOR TYPES DIFFERENCE OF TWO EVEN POWERS Slide 18: MORE COMPLICATED FACTOR TYPES FACTORING BY ADDING OR SUBTRACTING A CERTAIN TERM TO FORM A TRINOMIAL PERFECT SQUARE ADDING AND SUBTRACTING THE SAME TERM IS EQUIVALENT TO ADDING NOTHING, BUT THIS MAKES THE FORM FACTORABLE AS A DIFFERENCE OF TWO SQUARES. Slide 19: MORE COMPLICATED FACTOR TYPES FACTORING BY ADDING OR SUBTRACTING A CERTAIN TERM TO FORM A TRINOMIAL PERFECT SQUARE Slide 20: MORE COMPLICATED FACTOR TYPES FACTORING BY SYNTHETIC DIVISION OR TRIAL DIVISION WRITE DOWN ALL THE NUMERICAL COEFFICIENTS OF THE POLYNOMIAL, INCLUDING THE ZERO COEFFICIENTS. BY TRIAL AND ERROR, FIND A NUMBER WHICH WILL EQUATE THE LAST COLUMN TO ZERO. Slide 21: MORE COMPLICATED FACTOR TYPES FACTORING BY SYNTHETIC DIVISION OR TRIAL DIVISION COPY THE REMAINING NUMBERS EXCEPT THE ZERO ON THE LAST COLUMN. RECONSTRUCT THE POLYNOMIAL. THE DEGREE OF THE POLYNOMIAL MUST DECREASE BY ONE. Slide 22: MORE COMPLICATED FACTOR TYPES FACTORING BY SYNTHETIC DIVISION OR TRIAL DIVISION ROOT FACTOR IS: A+1 Slide 23: HIGHEST COMMON FACTOR OR HCF EXPRESSION OF HIGHEST DEGREE WHICH IS A FACTOR OF EACH GIVEN EXPRESSION. LOWEST COMMON MULTIPLE OR LCM EXPRESSION OF LOWEST DEGREE WHICH IS EXACTLY DIVISIBLE BY ALL OF THEM. Slide 24: HCF AND LCM You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
COLLEGE ALGEBRA 2 livycat Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 855 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: May 06, 2009 This Presentation is Public Favorites: 1 Presentation Description No description available. Comments Posting comment... By: rpriya (31 month(s) ago) Hi, can i get the copy of the ppt please. Saving..... Post Reply Close By: livycat (31 month(s) ago) I NEED YOUR E-MAIL ADDRESS. KINDLY POST IT HERE. Saving..... Edit Comment Close Premium member Presentation Transcript Slide 1: ALGEBRA Engr. Lizette Ivy G. Catadman Instructor / Lecturer LECTURE NOTES & PROBLEM SETS: PART 2 Slide 2: TYPE PRODUCTS SUM AND DIFFERENCE OF TWO TERMS (BINOMIALS) SQUARE OF A BINOMIAL Slide 3: TYPE PRODUCTS PRODUCT OF TWO BINOMIALS CASE 1 PRODUCT OF TWO BINOMIALS CASE 2 Slide 4: TYPE PRODUCTS CUBE OF A BINOMIAL SQUARE OF A TRINOMIAL Slide 5: TYPE PRODUCTS SQUARE OF A MULTINOMIAL PRODUCT OF A BINOMIAL AND A TRINOMIAL Slide 6: TYPE PRODUCTS BINOMIAL RAISED TO POWER n Slide 7: TYPE PRODUCTS BINOMIAL RAISED TO POWER n PASCAL’S TRIANGLE Slide 8: FACTOR TYPES COMMON FACTOR DIFFERENCE OF TWO SQUARES Slide 9: FACTOR TYPES PERFECT TRINOMIAL SQUARE SUM AND DIFFERENCE OF TWO CUBES Slide 10: FACTOR TYPES TRINOMIALS WITH DISTINCT FACTORS THE TRINOMIAL MUST BE ARRANGED IN DESCENDING POWERS OF THE GIVEN VARIABLE. IN THE ABOVE EQUATIONS, IT IS THE VARIABLE x. Slide 11: FACTOR TYPES TRINOMIALS WITH DISTINCT FACTORS IF THE LAST SIGN IN THE TRINOMIAL IS (+), THE SIGNS IN THE BINOMIAL FACTORS ARE THE SAME. IF THE MIDDLE TERM OF THE TRINOMIAL IS (+), THE SIGNS IN BOTH BINOMIALS ARE (+). IF THE MIDDLE TERM OF THE TRINOMIAL IS (-), THE SIGNS IN BOTH BINOMIALS ARE (-). Slide 12: FACTOR TYPES TRINOMIALS WITH DISTINCT FACTORS IF THE LAST SIGN IN THE TRINOMIAL IS (-), THE SIGNS IN THE BINOMIALS ARE DIFFERENT. TAKE THE PRODUCT OF THE INNER TERMS AND OUTER TERMS OF THE FACTORS (BINOMIALS). WHICHEVER HAVE THE HIGHER RESULT WILL CARRY THE SIGN OF THE MIDDLE TERM OF THE TRINOMIAL. Slide 13: MORE COMPLICATED FACTOR TYPES FACTORING BY REARRANGEMENT AND GROUPING CASE 1: IF A POLYNOMIAL HAS FOUR TERMS, IT MAY BE FACTORED OUT BY FIRST, SEPARATING IT INTO TWO GROUPS AND FACTORING EACH GROUP SEPARATELY. IF EACH OF THE TWO GROUPS HAS A COMMON FACTOR, THEN THE POLYNOMIAL CAN BE FACTORED OUT. Slide 14: MORE COMPLICATED FACTOR TYPES FACTORING BY REARRANGEMENT AND GROUPING CASE 2: IF A POLYNOMIAL HAS FOUR TERMS, SEPARATE THREE TERMS THAT WILL FORM A TRINOMIAL PERFECT SQUARE. IF THE EVENTUAL RESULT IS IN THE FORM OF THE DIFFERENCE OF TWO SQUARES, THE POLYNOMIAL CAN BE FACTORED OUT. Slide 15: MORE COMPLICATED FACTOR TYPES FACTORING BY REARRANGEMENT AND GROUPING CASE 1: CASE 2: Slide 16: MORE COMPLICATED FACTOR TYPES SUM AND DIFFERENCE OF TWO ODD POWERS DIFFERENCE OF TWO EVEN POWERS Slide 17: MORE COMPLICATED FACTOR TYPES DIFFERENCE OF TWO EVEN POWERS Slide 18: MORE COMPLICATED FACTOR TYPES FACTORING BY ADDING OR SUBTRACTING A CERTAIN TERM TO FORM A TRINOMIAL PERFECT SQUARE ADDING AND SUBTRACTING THE SAME TERM IS EQUIVALENT TO ADDING NOTHING, BUT THIS MAKES THE FORM FACTORABLE AS A DIFFERENCE OF TWO SQUARES. Slide 19: MORE COMPLICATED FACTOR TYPES FACTORING BY ADDING OR SUBTRACTING A CERTAIN TERM TO FORM A TRINOMIAL PERFECT SQUARE Slide 20: MORE COMPLICATED FACTOR TYPES FACTORING BY SYNTHETIC DIVISION OR TRIAL DIVISION WRITE DOWN ALL THE NUMERICAL COEFFICIENTS OF THE POLYNOMIAL, INCLUDING THE ZERO COEFFICIENTS. BY TRIAL AND ERROR, FIND A NUMBER WHICH WILL EQUATE THE LAST COLUMN TO ZERO. Slide 21: MORE COMPLICATED FACTOR TYPES FACTORING BY SYNTHETIC DIVISION OR TRIAL DIVISION COPY THE REMAINING NUMBERS EXCEPT THE ZERO ON THE LAST COLUMN. RECONSTRUCT THE POLYNOMIAL. THE DEGREE OF THE POLYNOMIAL MUST DECREASE BY ONE. Slide 22: MORE COMPLICATED FACTOR TYPES FACTORING BY SYNTHETIC DIVISION OR TRIAL DIVISION ROOT FACTOR IS: A+1 Slide 23: HIGHEST COMMON FACTOR OR HCF EXPRESSION OF HIGHEST DEGREE WHICH IS A FACTOR OF EACH GIVEN EXPRESSION. LOWEST COMMON MULTIPLE OR LCM EXPRESSION OF LOWEST DEGREE WHICH IS EXACTLY DIVISIBLE BY ALL OF THEM. Slide 24: HCF AND LCM