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Unformatted text preview: ! MATH114N-11400 Discussions Week 3 Discussion: Special Factoring Strategies January 2020 Account Syllabus Dashboard Courses Calendar Announcements Resources This is a graded discussion: 25 points possible due Jan 26 Week 3 Discussion: Special Factoring Strategies 71 Modules Required Resources Files Read/review the following resources for this activity: Grades Inbox " Home People Bookstore OpenStax Textbook Readings Lesson in Canvas Assignments in Knewton Help Factoring Trinomials with a Leading Coefficient of 1 Factoring Trinomials with a Leading Coefficient Other than 1 Factoring Special Products Choosing a Factoring Strategy Solving Quadratic Equations by Factoring Solving Polynomial Equations by Factoring Library Guides Media Gallery My Media New Webex Academic Support 95 Initial Post Instructions This week we continue our study of factoring. As you become more familiar with factoring, you will notice there are some special factoring problems that follow specific patterns. These patterns are known as: a difference of squares; a perfect square trinomial; a difference of cubes; and a sum of cubes. Choose two of the forms above and explain the pattern that allows you to recognize the binomial or trinomial as having special factors. Illustrate with examples of a binomial or trinomial expression that may be factored using the special techniques you are explaining. Make sure that you do not use the same example a classmate has already used! ! Follow-Up Post Instructions Respond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification. Writing Requirements Minimum of 3 posts (1 initial & 2 follow-up) with first post by Wednesday APA format for in-text citations and list of references Grading This activity will be graded using the Discussion Grading Rubric. Please review the following link: Link (webpage): Discussion Guidelines Course Outcomes (CO): 2, 3 Due Date for Initial Post: By 11:59 p.m. MT on Wednesday Due Date for Follow-Up Posts: By 11:59 p.m. MT on Sunday Unread Search entries or author $ % & Subscribed # Reply Prince Sekyi (Instructor) " Jan 19, 2020 Hello Class For this week we will be discussing about special factoring. These polynomials have a special ways of factoring them. Below is an example of factoring "sum of cubes". The pattern of factoring sum of cubes is (a3+b3 ) =(a+b)(a2-ab+b2). So in the example (27+x3 ), a=3 since 33=27 and b=x , putting the values at their appropriate places in the formula (a3+b3 ) =(a+b)(a2-ab+b2) gives the result below (27+x3 ) =(3+x)(9-3x+x2) You are required choose two of the special factoring listed below, get an example each of the two special factoring you choose and explain how to factor. a difference of squares; a perfect square trinomial; a difference of cubes; and a sum of cubes Note: When use the superscript feature on the tool bar to write your exponents. # Reply ' Kellie-Ann Kerr " Jan 21, 2020 The difference of square and the difference of cubes will be my two examples. The formula for difference of square is a2-b2=(a+b)(a-b) (Stapel, 2019). So for example if I would have to solve for x2-9, I would first put x2-32. Next I would start to factor by writing x2-9=(x+3)(x-3). This is how you would factor the difference of square. The formula for difference of cubes is a3-b3=(a-b)(a2+ab+b2) (Stapel, 2019). To solve for x3-33. First I would put x3-27=x3-33. Then I would move on to solving which would be (x-3)(x2+3x+32) then (x-3)(x2+3x+9). This is how you would solve for the difference of cubes. It is very important to remember the formulas given so you can just plug in the given numbers or variables and then solve. Reference Stapel, E. (2019). Special Factoring: Differences of squares. Purplemath. Retrieved from . Stapel, E. (2019). Sums and Differences of Cubes. Purplemath. Retrieved from . # Reply ' Prince Sekyi (Instructor) " Jan 21, 2020 Good job, Kellie-Ann She used difference of squares and difference of cubes. # Reply ' (1 like) Tritchann Bailey " Jan 23, 2020 Hi Mrs. Kerr I really enjoyed your post as I was able to fully understand both forms that you chose. Difference of squares and the difference of cubes. Your examples were very thorough and loved how you explained step by step. Great job! # Reply ' (1 like) Massiel Diaz " Jan 24, 2020 Hey Kellie, I read your explanation first and it was so accurate and clear, thanks for the references ill definitely check them out. # Reply ' Titilayo Akinyele " Jan 20, 2020 Hi everyone. Since we are going to be talking about some special ways of factoring this week, i will be working on the following two ways of special factoring. A sum of cube and a perfect square trinomial. First, starting with the way of factoring sum of cubes. Factoring sum of cube is when a two term expression were both cubes and have same sign. The formula is (a3+b3) =(a+b)(a2-ab+b2). For example (64+y3), where a=4 and 43=64 and b=y, insert the value in the right place, using the above formula to get this answer (64+y3)= (4+y)(42-4y+y2). The second special factoring i will be explaining is a perfect square trinomial. As we all know that a trinomial is a special trinomial, if their numbers can be factored into a binomial multiplied to itself. The formula is (a+b)2=a2+2ab+b2, (a-b)2=a2-2ab+b2. So using the example (y+8)2, where a=y, b=8, insert the values at the right places using the formula (a+b)2=a2+2ab+b2 we are going to get this answer y2+16y+64. # Reply ' Renee Connell " Jan 20, 2020 Hi Titilayo, I also talked about the sum of cube. I think that is one of the easiest signs to remember because as you and I both mentioned, it is when a two term expression are both cubes and have the same sign . With all of the different steps in math and different way to solve problems, I find this one of the easier things to remember. Factoring in math can be tricky, but once you memorize all the steps and makes it a lot less of a struggle. Great examples, Renee # Reply ' Titilayo Akinyele " Jan 20, 2020 Hi Renee Great. I can tell you one of the courses I have challenges on is mathematics. But what has always worked for me is time taking.Even when I got the answer wrong, I won’t give up till I got it right. Like you said, sum of a cube formula is easier to memorize. So is others. But I believe all we have to do is practicing, and solves more problems. # Reply ' Renee Connell " Jan 20, 2020 Same! Math does not come easy to me and the only way to get better is to keep practicing. I am the same way, I will not stop until I get the correct answer, no matter how long it takes me. Thanks! Renee # Reply ' Prince Sekyi (Instructor) " Jan 21, 2020 Good job, and example of 1. sum of cubes, 2. perfect square trinomial, # Reply ' Laura Agupusi " Jan 23, 2020 Hi Titilayo! I enjoyed how you presented the two equations for a sum of cubes and perfect square trinomial. I believe the equations help plug in the numbers (figures) into the equations rather than resulting in FOIL that can be confusing. Your examples also were very well explained and understanding that would be beneficial as we go more in-depth with more complicated questions. Also, we might need the formula as a step to step strategy that would be less confusing. # Reply ' Massiel Diaz " Jan 24, 2020 Hey Titilayo, Thanks for the review, I struggle with numbers ( math in general ) but you gave an accurate clear description with easy to follow steps. # Reply ' Adam Doyle " Jan 26, 2020 Thank you for the thorough response. I agree, that the sum of cubes is a really easy formula to memorize and to apply. To be honest, it is easier for me to comprehend things when I understand the formula, and (a3+b3)=(a+b)(a2-ab+b2) is a pretty easy formula to memorize. I discussed the sum of cubes as well, but you presented it a bit more eloquently. # Reply ' Renee Connell " Jan 20, 2020 Hello Everyone, As we continue to learn about factoring this week, I chose the difference of cubes and the sum of cubes to look more into. For difference of cubes, an example of a polynomial in this form would be x 3 – y 3 . With the difference of cubes, there is a rule to remember. The rule with the difference of two perfect cubes equals the difference of their cube roots multiplied by the sum of their squares and the product of their cube roots. Almost always with the difference of cubes, the sum is a factor of 3, unless it is a decimal or fraction. An example of using this method of solving a binomial is x 3 – y 3 = (x-y)(x2+xy=y2). Since the binomial is made up of two cube roots of the perfect cubes separated by a minus sign, the sum of the difference is solved using this method. If there is no cube,or if a factor is smaller than the largest cube on the list, then the number isn’t a perfect cube. Sum of cubes is a two term expression where both terms are a sum of cubes and both terms are cubes and each term uses the same sign. To start, you would figure out the greatest common factor of both numbers. Once you do that, you will then rewrite the expression using the GCF that you found with the numbers. For example, for the expression x3+64, you would find the GCF, which in this case is 4. You would then rewrite the problem as (x)3+(4)3. You would then use "square multiplied by square" which in this case would be x+4 4x x2 16 When using the sum of a cube, the first sign should always be the same as the original equation,so in this case the final answer would be (x+4)(X2-4X+16). # Reply ' Delvina Demirovic " Jan 20, 2020 Hello Class and Professor! When factoring the difference of squares, it is very eye catching to quick realize that you can square root a certain number. For example, if i see , i know that the square root of 25, is 5. I know this right off the bat, so it gives me a quicker way to realize what my next steps are. Then since this is the difference of squares, i know . Reference Academy, K. (2017). Difference of squares intro. Retrieved from Difference of squares intro | Mathematics II | High School Math | Khan Academy Another form of factoring is factoring a perfect square trinomial. An example of this would be . using the fomula a=x and b=5. Although, when looking at the expression, it is simple to see how there by be a relation between the square, the 10x, and 25. Now we know that . Clearly, just by glancing at an expression, we could realize a relation. Reference McLogan, B. (2015). How to factor a perfect square trinomial and why is it important. Retrieved from How to factor a perfect square trinomial and why is it important # Reply ' Brittany DelGado " Jan 20, 2020 Hi Delvina, I particularly thought that your response was very intersting. I thought that adding your videos and evidence of how to factor trinomials and differences of squares was also very intriguing because not only did you give examples but you also gave us as students a live video of how to solve these problems. Not only do I think the video was accptable but I also think that giving your own input on why you thought the difference of squares was intersting to you also shows that you are not afraid to show that you care about the assignment rather than reading off what you see. I enjoyed watching both videos! -Brittany # Reply ' (1 like) Emily Mongrella " Jan 22, 2020 Hi Delvina! I enjoyed watching these videos. I did my post from an article but it was cool to actually see someone do it. I picked the same two problems as well. The videos helped clarify somethings I could not understand while reading it. Thank you for your post! Emily Mongrella # Reply ' Katie Mason " Jan 22, 2020 Hi Delvina , I as well used an example involving difference of squares. You did a great job explaining how to factor this problem and i really like the videos. With these types of problems a visual is certainly a help. Also thank you for the example of the perfect square trinomial ! This was the last one i was thinking of doing and you helped clarify the steps for me. -Katie M # Reply ' Taurye Lugo " Jan 23, 2020 Hey Delvina, I just want to start off by saying that the examples of the square roots that you chose were easy for me to understand. I watched the links to the videos that you attached which also made it helpful for me to understand the formulas and how to factor the difference of squares as well as factoring a perfect square trinomial prior to coming to class on Friday. Thank you for this information and a very good job on this post! # Reply ' Tritchann Bailey " Jan 25, 2020 Hi Delvina, Great post, you post was very short but straight to the point. You were very thorough with your examples and explanations. Thanks for the clarification . # Reply ' Adam Doyle " Jan 26, 2020 Hi Delvina, Thanks for the great post. That video was really helpful. I recently began to utilize my calculator more than I previously had. It was really helpful when it comes to large scale factoring equations. I found that this video really broke it down into a step by step instructional process which made it seem a lot less confusing. Thanks, Adam # Reply ' Laura Cummings " Jan 26, 2020 Hi Delvina, I liked how your discussion showed videos on both difference squares and perfece square trinomials. You were able to discuss each topic, while having evidence on how to go about solving for each problem. To me, these are not easy questions, and seeing other examples by other teachers helps me figure out the equation or have a better understanding. I was able to learn more from your videos. # Reply ' Tamara Taylor Schenck " Jan 20, 2020 A Difference of Squares: by definition is the product of a sum of two numbers and their difference equals the difference of their squares( G. Rockswold,et.al., Beginning and Intermediate Algebra,2018.) For example (a+b) (a-b)=a2 - b2 . It's easy to recognize the difference of squares application because both sides are equal and when you factor out you will have (-) and (+) for each term. If your answer were to come out any other way it is not truly a difference of squares. ( A Sum of Cubes: by definition is a two term expression where both terms are cubes and each term has the same sign (J.White, Study.com, 2018.). For example a3 + b3 = (a+b) (a2 -ab+b2 ). This example clearly shows when factored out that both terms will be squared on each side plus one. References: Beginning and Intermediate Algebra (G. Rockswold, et.al., 2018.) Study.com ( J.White, 2018.) # Reply ' Brittany DelGado " Jan 20, 2020 Hi Tamara, I like how you described the definition of a difference of squares. This not only teaches the student what the square is, but it also give them an intro to what they are learning. I think that was a wonderful idea! I also like that you were able to include an example as how to solve the pronlem itself. You did a very good job in explaining what and how a student should recognize these problems in an equation. I particularly thought that it was intersting to read your input on the Sum of Cubes you were very clear in your writing and having examples of both of these types of problems really shows the reader you care. # Reply ' Prince Sekyi (Instructor) " Jan 21, 2020 Hi Tamara, That's a good explanation but you must write two examples with numbers like what I shown in my initial post. # Reply ' Titilayo Akinyele " Jan 23, 2020 Hi Tamara Read your post and i supported your ideas. Like you said, you can easily recognize square methods applications when their both sides are equal.And i also talked about sum of cubes. # Reply ' Prince Sekyi (Instructor) " Jan 24, 2020 Tamara You need to state examples using numbers, just like my initial post # Reply ' Brittany DelGado " Jan 20, 2020 Hi class, and Professor. For my assignment I will be starting off with Factoring a Trinomial with the leading coefficient of one. The second assigment that I chose is Factoring the sum and difference of cubes. I am firstly going to begin my discussion abot Factoring a trinomial with a leading coefficient of one. As Knewton explains there are many ways in which to find trinomials answer especially when it comes to factoring. However, it is different when it comes to a leading trinomial of only one. An example of this is x2+5x+6. This entire problem has a greatest common factor of 1. Another way of this equation being written is to write it as (x+2)(x+3). This way the student is able to recognize that there is not only one way to write equations like these but also that there can be two ways by breaking up the problem into two equations. Another example of this would be x2 + bx+c. These kind of problems can be solved by looking for the "product of c and a sum of b."(knewton). I feel like this video is a wonderful example of Factoring a Trinomial with a Leading Coefficient. Factoring a Trinomial with Leading Coefficient of 1 - The Basics Now going onto Factoring the Differences of Squares Knewton explains that the "perfect square" is a square minus a square that is "perfect." He explains that they can also be factored and have similar writings from the equation itself. They can also be written a different way but using completely different signs. An example of this is "a2-b2=(a+b)(ab)." Here is a video that also explains The Difference of Squares from Khan Academy Difference of squares intro | Mathematics II | High School Math | Khan Academy References: Factoring a Trinomial with Leading Coefficient of 1 - The Basics Difference of squares intro | Mathematics II | High School Math | Khan Academy # Reply ' Prince Sekyi (Instructor) " Jan 22, 2020 Hi Brittany, That's a good explanation but you must write two examples with numbers like what I shown in my initial post. You posted only one example with numbers thats , you need one more to have a complete initial post. # Reply ' Brittany DelGado " Feb 4, 2020 Hi Professor Sekyi, I don't think you saw, but I am glad to represent my equation to you again as I did include it in my initial post. This is my second equation that I put in my initial post. "a2-b2=(a+b)(a-b)." However, I do not think you saw it between the other videos I used to explain my problem. Best, Brittany Delgado # Reply ' Katie Mason " Jan 22, 2020 Hello Brittney! First off i really like the added video references, coming from a visual learner this is ...
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