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A Detailed Lesson Plan in Mathematics: Factoring Polynomials using Synthetic Division I. Learning Objectives At the end of the lesson the students should be able to: a. Factor Polynomials; b. Use synthetic division in factoring polynomials and; c. Appreciate the use of synthetic division in factoring. II. Subject Matter a. Topic: Factoring Polynomials using Synthetic Division b. References: https://youtu.be/vXcQ9f7p4jY c. Materials: Laptop and Google meet III. Procedure Teachers’ Activity Student’s Activity A. Preparation Greetings Prayer Announcement: Yesterday, you have answered your pretest already and I have here the result. Wherein, out of 10 result, the whole class average score is 5.38. It is not that bad, almost or higher half of the average score. By the way the pretest is a way to measure the things or part of the lesson that you already know in this subject. The important when we have are post-test, is that you will have higher score in it. B. Motivation So, let’s proceed now to our activity. Let’s have the KAHOOT, go to your google classroom wherein I give a link and it’s code(722493) you will join and play a kahoot, I know that you are all familiar with this game. Ok, so let’s start the game now! This is just a review of our previous topic that we have discuss last time. Duplicate of Synthetic Division (students started to join the game)
- Solve using synthetic division: (x³+3x+2) ÷ (x+1) Just click the right shape that correspond to your answer Choices: X+2 -x+ x-2 x+4 r 6 All have answer it already, so let’s see the correct answer! The answer is triangle (x+2) and 9 out of 13 got the correct answer. Very good! Let’s have our next question
- Solve using synthetic division: (x²+x-12) ÷ (x-3) Choices: X-4 x- X+4 x-2 r 6 All answered it already so, we can skip it again! And the answer is round X+4 and 7 got the correct answer! Let’s have the leaderboards! Christel got first with 1880 followed by Mark Luis with 1870 and then Ashley. In this game you will answer as fast as you can class to be on top! Let’s proceed now to question number 3.
- Solve using synthetic division: (x²+17x+60) ÷ (x+12) Choices: X-5 x+ X+4 x+ The answer here is square x+ and 6 got the correct answer! Let’s have the leaderboards! Mark Luis now is on top with 2909 followed by Jacob and Yohann. Let’s have now the fourth question:
going to factor polynomials in synthetic division. This are the topic involving factoring polynomials using synthetic division:
- If one of the factor is already given.
- If no factor is given. That will be our topic for this week. Ok! So, let’s have an example:
1. Find the missing factor of the polynomial equation. (6x²+x³-12+2x)÷(x+2) Our first step is to arrange the Polynomials or dividend in descending order, according to highest exponent up to the lowest exponent. We have here: x³+6x²+2x-12=(x+2). Then after that, we will get the factor of this one- of the dividend, the first factor is already given which is our divisor which is equal to (x+2), now to get the other factor we will apply synthetic division. So, we will equate the divisor by 0. x+2=0 then we will transpose positive two and it will become: X= -2, so x is -2 and it is the one which we will use, after that we will get the numerical coefficient of our dividend. It is: 1 6 2 -12, and now we will perform synthetic division: - 1 6 2 - -2 -8 12
remainder After you have got the quotient, we will get the depressed equation. How to get the depressed equation? We will look at the leading term of our dividend and it’s exponent. The exponent of the leading term is to the 3rd^ power or cube, so we will subtract it by 1 and it will become 2 or in the 2nd^ power. Then it will become: x². we will also deduct on the next term and it will become now: 4x and in the third term it will become constant which is -6. So, it will become now: x²+4x-6 and the remainder is 0. Therefore, our quotient is factor of the polynomial’s equation. So, the other factor of the polynomial equation is x²+4x-. Did you get it class? Ok! later you will be the one to explain. Now, let’s have our second example:
2. Find the missing factor of the given polynomial equation. (x³-18)=(x-2) x-2= x=2. Same process on what we did in example number 1 class. 2 1 0 0 - 2 4 8 Yes sir!
Alright! Start now. Ok! Very good! let’s clap for Mark Luis. He’s smart and ready! So, let’s have our next sample. Find the missing factor of the given polynomial equation: 3X³-17x²+22x-60=(x-5). (after a minute) Mark Luis is raising his hand again. Let’s give chance for others. So, let’s have Mica. 3X³-17x²+22x-60=(x-5). x-5= x=5. 5 3 - 17 22 - 15 - 10 60 First is, we will get the numerical coefficient sir and it is: 1 -4 4 - Then the x-3, we will equate it to zero to get the number which we are going to use as divisor and we have: x-3= x= On the process I will bring down 1 and multiply by 3 then I will add the product by 4. 3 1 -4 4 - 3 1 Repeat the process that I did on the first term, I will multiply -1 to the divisor which is 3 and I will do it on the rest term also until I get the answer. 3 1 -4 4 - 3 -3 3 1 -1 1 0 r So, the factor is (x²-x+1). (The students clap their hands)
3 -2 12 0 r ( 3 x²- 2 x+1 2 ). Ok! Start. Ok. Very good mica for sharing your knowledge. Class did you understand our topic already? D. Application Ok! So, let’s have your activity or challenge question for this topic. This July we are celebrating the National disaster Resilience Month. As a part of the preparation the Fire Chief of Imus City Department ask the Fire man to get the area of the base of the building. The building is a rectangular prism with a volume of X³-18x²+101x- 180 and its height (x-9). To get the divisor I will equate x-5 to 0. X-5= X= Then I will get the numerical coefficient of the dividend which is: 3 - 17 22 - Then I will solve now, I will bring down 3, then multiply to 5 and add the product to -17. After I got the sum, I will repeat the process I made in first term until I got their answers. 5 3 - 17 22 - 15 - 10 60 3 -2 12 0 r as you said during the discussion a while ago sir, if the remainder is 0, the polynomial is a factor. Therefore, the factor is ( 3 x²- 2 x+1 2 ). (The students make thumbs up)
Ok! The building based is equal to (x²-9x+20). Very good! how about the others, is your answer the same? Wow! My students are brilliant! E. Generalization Let’s generalize our topic for today. So, what have you learned from today’s lesson? Anyone who can summarize. What is our topic and the steps on computing the factors of the polynomial? Christel? Wow! Very good. So, now let’s integrate values in our topic. How can we relate factoring polynomials using synthetic division in real life situation? Anyone? Jin Sandagon? Ok! How about Kathrina? x-9= x=9. Let’s bring down 1 and multiply it to 9 then add the product to -18. 9 1 - 18 101 - 9 1 9 Let’s do it on the rest term what we did until we get the answer. 9 1 - 18 101 - 9 -81 180 1 9 20 0 r So, the factor is (x²-9x+20). Yes sir! What I learned about this topic is to factor polynomial using synthetic division. So, the first step is to factor the polynomials then, to use synthetic division in factoring polynomials and then, add and compute to get the answer. If the remainder is zero, then the polynomials is a factor. The engineer can use it in computing sir.
Ok! Just like life? Ok very good! For me, I want to share, our topic is like a life. We have the six factor or the ideal balance. The six factors Ideal Balance For us to be happy in our life the factors should be balance. We have spiritual, financial, emotional, personal, professional and physical. If we balance these, we have a happy life. That’s for me. Class, is our topic clear? Did you understand it? Ok! Very good. F. Evaluation So, Let’s have now our quiz. July is the National Nutrition Month. Do you know this year’s Nutrition Month Theme? Match column A to column B to get the missing factor. Write your corresponding answer on the space provided to decode this year’s nutrition month theme. Column A Column B
- x³+5x²+7x+3= (x+3)( ) Kumain ng wasto: x²+2x+
- 3x³-17x²+22x- 60=(x-5)( ) Push: x+
- x²+2x+1= (x+1)( ) at maging aktibo: 3x²-2x+
- x³-2x²-x+2= For me sir, if we can see in it’s step and follow it I can relate on how to do things we will do step by step so that the result will be good or right. Yes sir Yes sir!
Thank you and Goodbye sir!
