10 of 25 Mathematics 30-1: Module 3 6. Determine the degree, the leading coefficient, the constant, and the y-intercept for each of the following. a) P(x) = 4x' +(3.x?) -2x+7 (2 marks) b) P(x) = 4(2x-1)' -(x+3) (2 marks) c) P(x) = (x+3)'(x-2)(x+4) (2 marks) 7. Sketch the shape of the graph of each function with the given zeros. Assume a,, >0. Assume minimum degree. (6 marks) a) 0, -2, 3 b) 2 2 (multiplicity 2) c) 1 (multiplicity 2), 3, 5 8. Determine the minimum degree of the following polynomials. (2 marks) a b ) P(x) ( 4.8)Mathematics 30-1: Module 3 13 3. The polynomial shown at the beginning of the lesson could be written as P(x) = x3 + 3x - x - 3. ted from Stockbyte/Thinkstock Determine if each of the following binomials is a factor of the polynomial P(x) = x3 + 3x - x - 3? Explain your answers. a. x - 1 (2 marks) b. x + 1 (2 marks) c. x - 3 (2 marks) d. x + 3 (2 marks)\fMathematics 30-1: Module 3 10 Lesson 2: Factoring Polynomials 1. Completely factor each of the following polynomials. Begin by listing the possible integral zeros. a. P(x) = x - 4x + x + 6 (4 marks) Possible integral zeros:Mathematics 30-1: Module 3 3 c. h(x) = -2x + ax + x - 7, where aER i. sketch (2 marks) ii. end behavior (1 mark) iii. coordinates of the y-intercept (1 mark)Mathematics 30-1: Module 3 17 10. The volume of a rectangular prism is given by V(x) = x +3x -36x+32. Determine possible measures for w and h in terms of x if the length, I, is x-4. (2 marks)Mathematics 30-1: Module 3 15 7. When the polynomial 2x + bx -5 is divided by x-3, the remainder is 7. a) Determine the value of b. (2 marks) b) What is the remainder when the polynomial is divided by x-2? (1 mark) 8. Determine the value of k if x + 4 is a factor of P(x) = 3x' +1 1x2 -6x+k. (2 marks)Mdhemacs 30-1: Module 3 4 3. Without using technology, sketch the graphs tor each function provided and state the folbwing for each: s end behaviour I yintercept . xintercept(s) I multiplicity of each {actor Be sure to justify your answers mathematically. a. x} = {x + 2H1! 1}2 i. sketch (2 marks] ii. end behaviour [1 mark) iii . coordinates of the y-intercept [1 mark] iv. coordinates of the xinteroept(s) (2 marks] v. multiplicity of each factor (2 marks] 1 Search .II 7:03 AM 4 (I? Q 82% - m30_1_m3_revised... Mathematics 304: Module 3 1 MODULE 3: POLYNOMIAL FUNCTIONS Lesson 1: Sketching Polynomial Functions 1. Describe one advantage of the factored form of a polynomial function and describe one advantage oflhe expanded form of a polynomial function. [2 marks) 2. Will-tout using technology. draw a possible sketch for each function provided and state 1113 following for each: an and behaviour ' rinteroepi Be sure to justify your answers malhematically. a' x}: 3x2+5x+ T i. sketch {2 marks} ii' end behavior (1 mark) iii. coordinates of the y-intemept [1 mark} Mathematics 30-1: Module 3 c. h(x) = (x - a)(x - b)(x + c)?, where a > 0, b > 0, and c > 0 i. sketch (2 marks) X ii. end behvaviour (1 mark) iii. coordinates of the y-intercept (1 mark) iv. coordinates of the x-intercept(s) (3 marks) v. multiplicity of each factor (3 marks)Mathematics 30-1: Mom\" 3 19 2. While solving an equation of the town a):3 + lzm2 + G): + d = 0 {a.b.c.d E R ). a student created the following graph ol x} = a):5 + bx2 + car + d. y a. Describe hm\"r the graph can be used to determine the number of solutions on the interval 5