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Task 1. Write the factors of the following polynomials Task 2. A. Find the greatest common factor of the terms in each polynomial below. B. Factor each of the following polynomials. 5.) 2x + 8 6.) 12 + 24x 7.) 8x2 + 4x 8.) 7x3 - 213-:2 9.) x3 - x5 + x4 10.) a12 - a1\" + a8 Task 3. Factor the polynomials below. 1.) X2 - 64 2.) X2 - 25 3.) 9x2 - 4 4.) 4m3 - 16m 5.) 81x2 - 4964 Task 4. Factor the polynomials below. 1.) M2 + 14m + 49 2.) 4x2 + 4x + 1 3.) 9x2 + 30x + 25 4.) 25x2 - 10xy + y2 5.) 4a2 - 36a + 81 Task 5. Factor as completely as possible. 1.) X2 - 4x - 21 2.) X7 - 5x6 - 14x5 3.) 2m2 - m - 1 4.) 3x2 + 10x + 7 5.) 12p2 + 7pq - 12q2Task 6. 1.) Is x3 +1 a monomial, binomial, or trinomial? 2.) Give the degree of x2 - 17): + 2x3 - 5. 3.) Factor each of the following polynomials. a. 20):3 -10x2 - 30 b. x2+8x+ 16 c.2x2-19x+42 d.2m3-50m e. 64x2-81z2 f. (y+ 1)2- 16 g.9x4-81 h. 6x2+11ab- 28b2 i. 4x2+5x+1 Task 7. Match column A with column B by connecting their correSponding points with a line. Every time you match, a letter crossed, put the letter in the box below Corresponding to the number of the expressions. (It's in the picture) Match Column A with column B by connecting their corresponding points with a line. Every time you match, a letter crossed, write this letter in the box below corresponding to the number of the expressions. INTOFED A B 1. x' + 6x - 7 S (x - 5) P (x - 5) 2. x' -4x + 4 R G (x - 8) (x+ 5) task 7 3. x2 - 5x + 40 (X - 11 ) (x + 10 4. X2 -10x + 25 H (x + 7) (X - 1) 5. X2-X -110 ( X - 2) ( X - 2 ) NTask 6. 1.) Is x3 +1 a monomial, binomial, or trinomial? 2.) Give the degree of x2 - 17): + 2x3 - 5. 3.) Factor each of the following polynomials. a. 20):3 -10x2 - 30 b. x2+8x+ 16 c.2x2-19x+42 d.2m3-50m e. 64x2-81z2 f. (y+ 1)2- 16 g.9x4-81 h. 6x2+11ab- 28b2 i. 4x2+5x+1 Task 7. Match column A with column B by connecting their correSponding points with a line. Every time you match, a letter crossed, put the letter in the box below Corresponding to the number of the expressions. (It's in the picture) Task 8. Solve for the unknown 1.)P(6,6)=___ 2.)P(7,r)=840 3.)P(n,3)=60 4.)P(n,3)=504 5.)P(10,5)=___ 6.)P(8,r)=6720 7.)P(8,3)=__ 8.)P(n,4)=3024 9.)P(8,3)=1320 10.)P(913,r)=156 Task 9. Solve the following. 1. Anna have 8 T-shirt, 5 pair of pants and 3 pairs of shoes. In how many ways she can dressed herself for the day? 2. The school canteen offers student meal. In how many ways can a student select his meal if they offer 3 different kinds of rice, 5 main dishes, 3 vegetable dishes, 4 different juices. 3. A dress shop owner has 8 new dresses that she wants to display in the window, if the display window has 5 mannequins, in how many ways can she dress them up? Task 10: Can you show me the way? A. A close friend invited Anna to her birthday party. Anna has 4 new blouses (stripes, with ruffles, long-sleeved, and sleeveless) and 3 skirts (red, pink, and black) in her closet reserved for such occasions. 1. Assuming that any skirt can be paired with any blouse, in how many ways can Anna select her outfit? List the possibilities V 2. How many blouse-and-skirt pairs are possible? 3. Show another way of finding the answer in item 1. B. Supposed you secured your Bike using a combination lock. Later, you realized that you forgot the 4-digit code. You only remembered that the code contains the digits 1,3,4, and 7. 1. List all the possible codes out of the given digits. 2. How many possible codes are there? 3. What can you say about the list you made? A Questions: a. How did you determine the different possibilities asked for in the two situations? What methods did you use? b. What did you feel when you were listing the answers? Task 11: Count me in! Answer the following questions. 1. Ten runners join a race. In how many possible ways can they be arranged as first, second and third placers? 2. Ifjun has 12 T-shirts. 6 pairs of pants. And 3 pairs of shoes. How may possibilities can he dress himself up for the day? 3. In how many ways can Aling Rosa arranged 6 potted plants in a row? 4. How many four-digit numbers can be formed from the numbers 1.3.4.6,8, and 9 if repetition of digits is not allowed? 5. Suppose that in a certain association, there are 12 elected members of the Board Directors. In how many ways can a president, a vice president, a secretary, and a treasurer be selected from the board? -THE PRINCIPLE BEING APPLIED HERE IS THE FUNDAMENTAL COUNTING PRINCIPLES In the activity you have done, wereyou able to determine the exact number of ways of doing each task or activity describe? What mathematical concept or principle did you used? How was that principle applied? Some of this tasks or activities share similarities or differ from others in some sense, The principle being applied here is the Fundamental Counting Principles, It states that if activity A can be done n, ways, activity B can be done in ne ways, activity C can be done in ne ways, and so on, then activities A,B,C can be done in my . na. ns . ways. In the above activities or task, arrangement or order of selecting the objectsis important; that is whether a different order or arrangement means different result. A Permutation is an arrangement of things in a definite order of the ordered arrangementof distinguishable objectswithout allowingrepetitions among the objects. In general, if n is a positive integer, then n factorial is the productof all the integersless than or equal to n. ni = n. (n-1). (n-2). ...2.1 As an special case Of = 1 How do we find the permutation of objects? ILLUSTRATIVE EXAMPLE 1. Suppose we have 6 potted plants and we wish to arranged 4 of them in a row, In how many ways can this be done? We can determine the number of ways these plants can be arranged in a row if we arrange only 4 of them at a time.Each possible arrangement is called Permutation. The permutation of 6 potted plants taken 4 at a time is denoted by P(6, 4), 6P4 , or P.. similarly, if there are n objects which will be arranged r at a time, it will be denoted by P(n,r) THEREFORE: P(6,4)= 6 . 5 . 4 . 3= 360 WAYS ILLUSTRATIVE EXAMPLES 2 In how many ways can 5 people arranged themselves in a row for picture taking? Solution n= 5, 1=5 3