MHF4U Lesson 16 Assignment In this assignment you are going to explore the characteristics of polynomials functions. Part A: Finding the Answer In this section, you are going to use the clues provided for you in the lesson to answer these questions For each question, answer the question giving the strategies that you used in determining your answer. You will be given six marks - four marks for your strategy and two marks for the correct answer. Problem 1. Factor 2x* - 7x -41x- -53x - 21 fully. MHF4U Lesson 16 Page 1 2. Prove that x2 + 5x + 6 is a factor of x4 + 5x + 2x2-20x -24. 3. Solve 2x4 - x3 = 7x2 - 9x + 3.4. Amit has designed a rectangular storage unit to hold large factory equipment. His scale model has dimensions I'm by 2 m by 4 m. By what amount should he increase each dimension to produce an actual storage unit that is 9 times the volume of his scale model? (include a diagram)_ MHF4U Lesson 16 Page 3 5. Maria is designing a series of stationary trays for holding papers and envelopes. Each tray starts as a rectangular sheet of metal from which identical squares are cut from the four corners. The resulting rectangular flaps are then folded up and welded to produce an open-topped rectangular tray. What size of square should Maria cut from a rectangular sheet of metal 15 cm by 25 cm in order to produce a tray with a volume of 476 cm_? (include a diagram)6. The distance ofa ship from its harbour is modelled by the function d(t) = -3t3 + 3t2+18t where t is the time elapsed in hours since departure from the harbour. (draw a diagram to illustrate the problem) a} Factor the time function. b) When does the ship return to the harbour? c) There is another zero of d(t). What is it and why is it not relevant to the problem?I d) Draw a sketch ofthe function where 0 g 1' 3 . e} Estimate the time that the ship begins its return trip back to the harbour. l'"""-"""""-""\"""""\"-""""""""-""""""""""""""1 |_ ___ __ _____ _____ __ ___ __ ___ __ ___ __ ___ __ ___ __ ___ __ ___ __ ___ __ ___ __ ___ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I