X - Math Empowerment the A. Determine if the statement is true or false. Write T If the statement is true, and F if it is false. 1. Both long division and synthetic division can be used to divide a polynomial P(x) with a divisor that has a greater degree than P(x). 2. It is impossible to determine the remainder when dividing a polynomial P(x) by a divisor D(x) of degree lesser than P(x), when using synthetic method. 3. In the equation, 2a' + 110 - 3a + 16 = (a + 6)(2a -a +3) -2, -2 is the remainder when 2a' + 1la - 3a + 16 is divided by a + 6. 2x + 3 4. The degree of the remainder is always less than the degree of the divisor. is 5. Synthetic division cannot be used in dividing polynomials when the divisor is of the form ax + b. B. Find the quotient of the following using long division method. to be 1. (x) + 8x3 - 20x) + (x - 2) 4 -10x 2. (9b3 + 56 - 8) + (3b -2) 1362 + 2b +3 3. (2x* - x' - 9x7 + 4) + (x2 + 4) 1x - x- 1 4. (60# + cl - 20' + C + 1) + (20' + c-2) 5. (27 + 2' + 1) + (27 + 22# - 1) 6. (m - 4m' + 5m - m' + 1) + (m3 - 1) 7. (6/ -171 +271 - 417 +567 -46/ 4 15) - (212 -51+4)3. Dengue outbreak has been rampant during rainy seasons. It is estimated that the number of students at a particular high school who will catch dengue during the 150t2 outbreak is given by n = 12 + 1 where t is the number of weeks from the beginning of the outbreak and n is the number of affected students. Determine how many students will get ill during the first week of the outbreak. 4. Find two polynomials such that the resulting quotient is given by y' - 6y + 9 - - 1 y - 3 5. Find the value of d such that 4x3 + 4x2 - 76x - d is exactly divisible by x - 4. Math Ideas Come up with your own Mind-Reading-Number-Trick similar to the one in Math Investigation by applying the concepts of dividing polynomials. Present your your trick if it works.8. 5x - 3 D. Answer the following. 1. What is z - 2z + 4z - 3 divided by z - 1? 2. What is the remainder when 2y3 + y? - 5y + 2 is divided by y + 2? 3. Find the quotient when 2x - 1 is divided by 2x + 1. 4. Is z - z + 1 exactly divisible by 4z - 1? 5. What is the difference between synthetic division and long division in dividing polynomials? E. Read and solve each word problem. Show your complete solutions. 1. If the volume of a box is x3 + 10x + 31x + 30 and its height is given by x + 2, find the expression that represents the product of its length and width. 2. In economics, the average cost or unit cost is equal to the total cost divided by the number of goods produced. A local yema factory estimates that its cost is 0.03x2+ 400x + 10 000 to produce x units of yema. Determine the average cost in producing 500 yema candies. 60 Math for 1C. Use synthetic division to find the quotient. 1. P(x) = 2x3 + 7x - 6x - 8; D(x) = X +4 2. P(x) = 3x7 + 5x" - x + 3; D(x) = x + 1 3. P(x) = 6x5 - 4x2 4 2x - 3; D (x) = 2x - 1 4. P(x) = x' - 3x - 1; D(x) = x + 3 5. P(x) = X - 7x3 +x+1; D(X) = x+3 6. x +5 x + 2 7. 3x3 - 5x2 + 4x + 2 3x + 1 8. 10x - 26x + 22x - 26x + 12 5x - 3 D. Answer the following. 1. What is 23 - 2z2 + 4z - 3 divided by z - 1? 2. What is the remainder when