Chapter Prerequisite Skills BLM 1.. Evaluate Functions 1. Given P(x) = x 4 x + 5x 11, evaluate. a) P( ) b) P() c) P( 1) 1 d) P 4 Simplify Expressions. Expand and simplify. a) (x x x + 4)(x 1) + b) (x + x 4x )(x + ) 5 c) (x 6)(x + 6) d) (x 7)(x + 7) e) (x + 5)(x + + 5) Factor Expressions. Factor fully. a) x 49 b) 64a 11b c) m 75n d) 5x 4 5 4. Factor each trinomial. a) b b 15 b) m 9m +18 c) a 5a 1 d) x 17x + 10 e) 6x 5x 4 Determine Equations of Quadratic Functions 7. Determine an equation for the quadratic function, with the given zeros, that passes through the given point. a) zeros: and 5; point (1, 1) b) zeros: 6 and 0; point (, ) c) zeros: 5 and 1 ; point ( 1, 48) Determine Intervals From Graphs 8. For the graph of each polynomial function, i) identify the x-intercepts ii) write the interval(s) for which the graph is above the x-axis and the interval(s) for which the graph is below the x-axis. a) b) Solve Quadratic Equations 5. Solve by factoring. a) x x 5 = 0 b) 5x 16x + = 0 c) 18a 50 = 0 d) 6x x = 18 e) 10x 7 = 9x 6. Use the quadratic formula to solve. Round answers to one decimal place. a) x 5x + 1 = 0 b) x + 6x 7 = 0 c) 7x + 1 = 4x BLM 1 Prerequisite Skills
.1 The Remainder Theorem BLM.. 1. a) Divide x x + x 6 by x +. Express the result in quotient form. b) Identify any restrictions on the variable. c) Write the corresponding statement that can be used to check the division. d) Verify your answer.. Perform each division. Express the result in quotient form. Identify any restrictions on the variable. a) x + x 5x + divided by x + b) 4x + x 4 divided by x + 1 c) 6x 9x 4 + 6x 5 divided by x d) 8x 10x 1 divided by x. Determine the remainder R so that each statement is true. a) (x )(x + 1) + R = 6x x 7 b) (x + 5)(x 1)(x + 4) + R = x + 17x + 1x 10 4. The area, in square centimetres, of the base of a square-based box is 4x 1x + 9. Determine possible dimensions of the box if the volume, in cubic centimetres, is 4x 8x + 57x 6. 7. For what value of k will the polynomial f(x) = x + x + kx + 5 have the same remainder when it is divided by x + 1 and x? 8. Use the remainder theorem to determine the remainder when x 4 + x x + 6 is divided by x. 9. a) Use the remainder theorem to determine the remainder when 4x +x 6x + 1 is divided by x 1. b) Verify your answer in part a) using long division. c) Use Technology Verify your answer in part a) using technology. 10. a) Determine the remainder when 8x + x x is divided by x + 1. b) Factor 8x + x x fully. 11. When the polynomial mx + 5x nx 1 is divided by x 1, the remainder is. When the same polynomial is divided by x +, the remainder is 10. Determine the values of m and n. 5. Use the remainder theorem to determine the remainder for each division. a) x x + 5x divided by x 4 b) x + x 4x + 10 divided by x + c) x 4 + x x + divided by x + 6. a) Determine the value of c such that when P(x) = x cx + 4x 7 is divided by x, the remainder is. b) Use Technology Verify your answer in part a) using a computer algebra system. BLM Section.1 Practice
. The Factor Theorem BLM.. 1. Determine if x is a factor of each binomial. a) x x + x b) x + x 16 c) x x + x 6. List the values that could be zeros of each polynomial. Then, factor the polynomial. a) x x x + b) x 7x 6 c) x + 5x x 4. Factor each polynomial by grouping terms. a) x + x 9x 18 b) x + 5x 8x 0 c) x x 5x + 75 d) x 5x 7x + 45 4. Determine the values that could be zeros of each polynomial. Then, factor the polynomial. a) x + x 10x + 8 b) x + 5x + x c) x + x 5x 6 d) x 16x + x 6 5. Factor each polynomial. a) x + 5x x 5 b) x 7x + 6 c) x x 4x + 1 d) x 4 + 4x x 16x 1 e) x 4 x 14x + 48x 6. Use Technology Factor each polynomial. a) x + x 11x 6 b) 4x 9x 10x + c) 5x 1x 6x + 16 7. Determine the value of k so that x is a factor of x x + kx 6. 9. A carpenter is building a rectangular storage shed whose volume, V, in cubic metres, can be modelled by V(x) = 4x 6x + 107x 105. a) Determine the possible dimensions of the shed, in terms of x, in metres, that result in the volume in part a). b) What are the dimensions of the shed when x = 5.? 10. Factor each polynomial. a) x + 11x + x 15 b) x + 8x + x c) 5x 17x + 16x 4 d) 4x + 5x x 6 11. Factor each polynomial. a) 8x 15 b) 64x 8 + 7 c) 16x + y d) 7 t 6 e) 15x 6 1 y 64 f) 8x 6 + 4y 1 1. Factor each polynomial by letting t = x. a) 16x 4 17x + 1 b) 9x 4 61x + 100 1. Determine a polynomial function P(x) that satisfies the following set of conditions: P() = P = P( 4) = 0 and P() = 7. 14. Factor. x 5 x 4 x 4x + 19x + 6 8. Determine the value of k so that x + 5 is a factor of 4x kx 6x + 10. BLM Section. Practice
. Polynomial Equations BLM 5.. 1. Solve. a) x 4x + x = 0 b) x + x 18x 9 = 0 c) x x 1x + 8 = 0. Solve. a) x x 11x + 6 = 0 b) x x 17x 15 = 0 c) 8x 6x x + 1 = 0. Use the graphs to determine the roots of the corresponding polynomial equations. The roots are all integral values. a) Window variables: x [ 7, 7], y [ 0, 0], Yscl = 5 b) Window variables: x [ 7, 7], y [ 0, 40], Yscl = 5 c) Window variables: x [ 7, 5], y [ 10, 10] 4. Determine the real roots of each polynomial equation. a) (x 1)(x + x + 4) = 0 b) (x + 5x + 10)(x 5) = 0 c) (4x 64)(5x + 5) = 0 d) (x 1)(x 7) = 0 5. Determine the x-intercepts of the graph of each polynomial function. a) f(x) = x 1 b) g(x) = x + x + 4x + 1 c) h(x) = x 5 9x + 8x 7 d) y = x 4 5x + 144 6. Solve. a) x x 5x + 6 = 0 b) x 4 x 10x 8x = 0 c) 5x 5 80x = 0 d) x + x x 1 = 0 e) x + 7x = 4 f) x 4 6x + 5 = 0 7. Use Technology Solve. Round answers to two decimal places. a) x + x + 7x 1 = 0 b) x 4 6x + x = c) x 4x = x 8 d) 4x 4 6x x 4 = 0 8. Use Technology A rectangular water tank in an aquarium has width x 5, length x + 4, and height x, with all the dimensions in metres. If the volume of the tank is 110 m, use technology to solve a polynomial equation in order to determine the approximate dimensions of the tank, to two decimal places. 9. The length of a child s square-based jewellery box is 5 cm more than its height. The box has a capacity of 500 cm. Solve a polynomial equation to determine the dimensions of the box. 10. Find all real and complex solutions to x + 1x + 1x 8 = 0. 11. Determine a polynomial equation of degree with roots x = 5 and x = 7 ± i. BLM 5 Section. Practice
.4 Families of Polynomial Functions BLM 6.. (page 1) 1. The zeros of a quadratic function are 5. Which of the following polynomial and 5. functions belong to the same families? a) Determine an equation for the family Explain. of functions with these zeros. A y = 0.8(x 4)(x + 1)(x + ) b) Write equations for two functions with these zeros. B y = (x 1)(x + )(x + 4) c) Determine an equation for the member of the family that passes through the point ( 1, 6).. Examine the following functions. Which function does not belong to the same family? Explain. A y = 4(x + 1)(x 5)(x + 7) B y = 4(x 5)(x + 1)(x + 7) C y = 4(x 5)(x + 7)(x + 1) D y = 4(x + 7)(x 1)(x 5). The graphs of three polynomial functions are given. Which graph represents a function that does not belong to the same family as the other two? Explain. A Window variables: x [ 7, 7], y [ 0, 0], Yscl = B Window variables: x [ 7, 7], y [ 10, 10] C y = 0.8(x 4)(x + )(x + 1) D y = 0.5(x + 1)(x 4)(x + ) E y = (x 1)(x + 4)(x + ) F y = (x + )(x 1)(x + 4) 6. a) Write an equation for a family of functions with each set of zeros. i) 5,, 7 ii) 6,, iii) 4, 1,, 5 b) Determine an equation for the member of the family that passes through the point (1, 8) for each equation in part a). 7. a) Determine an equation for the family of cubic functions with zeros,, and 5. b) Write equations for two functions that belong to the family in part a). c) Determine an equation for the member of the family whose graph has a y-intercept of 10. d) Sketch a graph of the functions in parts b) and c). C Window variables: x [ 7, 7], y [ 10, 5] 8. a) Determine an equation for the family of quartic functions with zeros 4, 1, 0, and. b) Write equations for two functions that belong to the family in part a). c) Determine an equation for the member of the family whose graph passes through the point (, 6). d) Sketch a graph of the functions in parts b) and c). 4. Determine an equation for the function that corresponds to each graph in question. BLM 6 Section.4 Practice
9. a) Determine an equation for the family of cubic functions with zeros, 1, and 5. b) Determine an equation for the member of the family whose graph passes through the point ( 1, 8). c) Sketch a graph of the function in part b). 10. a) Determine an equation, in simplified form, for the family of cubic functions with zeros and 4 ±. b) Determine an equation for the member of the family whose graph passes through the point (1, 18). 11. Determine an equation for the cubic function represented by this graph. BLM 6.. (page ) 1. An open-top box is to be constructed from a square piece of cardboard that has sides measuring 0 cm each. It is constructed by cutting congruent squares from the corners and then folding up the sides. a) Express the volume of the square-based box as a function of x. b) Write an equation to represent a box with a volume that is i) one-half the volume of the box represented by the function in part a) ii) three times the volume of the box represented by the function in part a) c) How are the equations in part b) related to the one in part a)? d) Sketch graphs of the functions from parts a) and b) on the same coordinate grid. e) Determine possible dimensions of the box that has a volume of 178 cm. 14. a) Write an equation for a family of odd functions with three x-intercepts, two 5 5 of which are and. b) Determine an equation, in simplified form, for the member of the family in part a) that passes through the point (, 66). c) Determine an equation, in simplified form, for the member of the family in part b) that is a reflection in the x-axis. d) Is the function in part c) an odd function? Explain. 1. a) Determine an equation, in simplified form, for the family of quartic functions with zeros 1 (order ) and ± 5. b) Determine an equation for the member of the family in part a) whose graph has a y-intercept of 1. BLM 6 Section.4 Practice
.5 Solve Inequalities Using Technology BLM 7.. (page 1) 1. Write inequalities for the values of x 5. For each graph write shown. i) the x-intercepts a) ii) the intervals of x for which the graph is positive. iii) the intervals of x for which the graph b) is negative. a) Window variables: x [ 6, 6], y [ 5, 15] c) d). Write the intervals into which the x-axis is divided by each set of x-intercepts of a polynomial function. a) 7, 1 b), 4 c), 6, 0. Describe what the solution to each inequality indicates about the graph of y = f(x). a) f(x) > 0 when < x < 1 or x > b) f(x) 0 when x 0 or 0 x 4. Sketch a graph of a quartic polynomial function y = f(x) such that f(x) > 0 when.5 < x < 0.5 or 1 < x < and f(x) < 0 when x <.5 or 0.5 < x < 1 or x >. b) Window variables: x [ 8, 6], y [ 10, 10] c) Window variables: x [ 6, 6], y [ 10, 10] d) Window variables: x [ 6, 6], y [ 10, 10] 6. Solve each polynomial inequality by graphing the polynomial function. a) x x 8 0 b) x + 7x + 6 > 0 c) x + x 16x 16 0 d) x x 5x + 6 < 0 e) x 4x 11x + 0 0 BLM 7 Section.5 Practice
7. Solve each polynomial inequality. Use a computer algebra system, if available. a) x 5x < 0 b) 4x 8x + 45 0 c) x 4x + x + 6 > 0 d) x + x 9x 9 0 e) x 6x x + 0 0 8. Use Technology Solve each polynomial inequality by first finding the approximate zeros of the related polynomial function. Round answers to two decimal places. a) x 5x + 1 0 b) x + x x 1 < 0 c) 4x x + 5 > 0 d) x + x 4x 6 0 e) x 4 5x 4x + 5 < 0 BLM 7.. (page ) 10. The height, h, in metres, of a golf ball t seconds after it is hit can be modelled by the function h(t) = 4.9t + t + 0.. When is the height of the ball less than 10 m? Round to two decimal paces. 11. The solutions given correspond to an inequality involving a quartic function. Write a possible quartic polynomial inequality. x < 5 or < x < 5 or x > 7 1. Use Technology Solve. Round answers to two decimal places. x 4 + 8x + x 10 10x 4 + x 8x 4 9. Solve. Round answers to one decimal place. a) x x 1x 1 > 0 b) x + x + x < 0 c) x + 10x 5 0 d) x 4 + 6x x + x 10 0 BLM 7 Section.5 Practice
.6 Solve Factorable Polynomial Inequalities Algebraically BLM 8.. 1. Solve each inequality. Show each solution on a number line. a) x > 7 b) x 5 c) 5x 11 > x + 1 d) 4( x) x 6. Solve by considering all cases. Show each solution on a number line. a) (x + )(x ) 0 b) (x + 1)(x ) < 0. Solve using intervals. Show each solution on a number line. a) (x + 4)(x 5) > 0 b) (x + )(x 1) 0 4. Solve. a) (x + )(x 4)(x 6) 0 b) (x + 5)(x 1)(x ) 0 c) (1 x)( x + )(x ) > 0 d) ( x)(x + 1)(x ) < 0 7. Solve. a) x x 4 < 0 b) x + 6x + 11x + 6 0 c) x + 7x x > 0 d) x + 5x x 8 0 8. A certain type of candle is packaged in boxes that measure 6 cm by 15 cm by 8 cm. The candle company that produced the above packaging has now designed shorter candles. A smaller box will be created by decreasing each dimension of the larger box by the same length. The volume of the smaller box will be at the most 90 cm. What are the maximum dimensions of the smaller box? 9. Solve using intervals. x 4 + 10x + 1 x 5 + 15x + 8x 5. Solve by considering all cases. Show each solution on a number line. a) x + x 10 < 0 b) x + 10x + 1 0 c) x + x x 0 d) x x 1x + 4 > 0 6. Solve using intervals. a) x x 5x + 6 0 b) x + 5x x 8 > 0 c) x 5x + x < 0 d) x 4 1x 1x 0 BLM 8 Section.6 Practice Copyright 008 McGraw-Hill Ryerson Limited
Chapter Review BLM 9.. (page 1).1 The Remainder Theorem. Polynomial Equations 1. i) Use the remainder theorem to 9. Use the graph to determine the roots of determine the remainder for each the corresponding polynomial equation. division. Window variables: x [ 6, 6], ii) Perform each division. Express the y [ 5, 5], Yscl = 5 result in quotient form. Identify all restrictions on the variable. a) x + 4x divided by x b) x 5x + x 6 divided by x 5 c) x 4 x 4x + 5x 15 divided by x + 1. a) Determine the value of k such that when f(x) = x 5 4x + kx 1 is divided by x +, the remainder is 5. b) Use Technology Verify your answer in part a) using technology.. For what value of m will the polynomial P(x) = x + mx 4x + 1 have the same remainder when it is divided by x + and by x?. The Factor Theorem 4. List the values that could be zeros of each polynomial. Then, factor the polynomial. a) x + x 10x + 8 b) x + 7x + 7x + c) x 4 + x 14x 4x + 8 5. Factor each polynomial. a) x x 9x + 7 b) 4x + 4x 5x 5 c) 9x + 18x 4x 8 6. Determine the value of b such that x + 4 is a factor of x 4x + bx 8. 7. Determine the value of k such that x is a factor of x + kx 5x +. 8. A rectangular box of crackers has a volume, in cubic centimetres, that can be modelled by the function V(x) = x x + 00x 800. a) Determine the dimensions of the box in terms of x. b) What are the possible dimensions of the box when x = 5? 10. Determine the x-intercepts of each polynomial function. a) y = 7x 64 b) f(x) = x x + 16x c) g(x) = x 4 9x + 100 11. Determine the real roots of each polynomial equation. a) (x x 10)(x + 8) = 0 b) (5x 15)(x 81) = 0 1. Use Technology Solve. Round answers to two decimal places. a) 5x + x + x + 10 = 0 b) 5x x = 18 9x c) 4x 4 + x + x 1 = 0 1. Use Technology A small doll house has dimensions such that the width is 6 cm less than the height and the length is cm less than 1.5 times the height. a) Write an equation for the volume of the house. b) Find the possible dimensions of the house, to two decimal places, if the volume is 8500 cm..4 Families of Polynomial Functions 14. a) Determine an equation for the family of cubic functions with zeros 1,, and 6. b) Write equations for two functions that belong to the family in part a). c) Determine an equation for the member whose graph passes through the point ( 1, 4). BLM 9 Chapter Review
15. a) Determine an equation, in simplified form, for the family of cubic functions with zeros and 1 ± 6. b) Determine an equation for the member of the family whose y-intercept is 10..5 Solving Inequalities Using Technology 16. Use Technology Solve. Round answers to two decimal places, if necessary. a) x 5x + 4x 0 b) x + 4x > 0 c) x 4 + 5x x + x 0 d) 4x 5 + 7x x + 10 < 0 BLM 9.. (page ).6 Solve Factorable Polynomial Inequalities Algebraically 18. Solve each inequality. Show the solution on a number line. a) (4x + 5)(x + ) 0 b) (x 1)(x + 5)( x) 0 c) (4x 9)(x + 6x + 9) > 0 19. Solve. a) x x 15 < 0 b) x x + 9x + 9 > 0 c) x 4 4x 1x + 100x 100 0 17. Sketch a graph of a cubic polynomial function y = f(x) such that f(x) < 0 when x < 5 or < x < and f(x) > 0 when 5 < x < or x >. BLM 9 Chapter Review
Chapter Test BLM 11.. (page 1) For questions 1 to, select the best answer. 7. Use the graph to determine the roots of 1. Which of the following is not a factor of the corresponding polynomial equation. x x 18x + 9? Window variables: x [ 6, 6], A x + y [ 0, 10], Yscl = B x C x + 1 D x 1. Which statement is false for P(x) = x + 11x 19x + 10? A P(x) = (x + 1)( x + 1x ) + 4 B x 5 is a factor of P(x). C When P(x) is divided by x, the remainder is 10. D x is a factor of P(x).. The values that could be zeros for the polynomial x x 19x + 0 are A ± 1, ± 4, ± 5 B ± 1, ±, ± 4, ± 5, ± 10, ± 0 C ± 1, ±, ± 4, ± 5 D ± 1, ±, ± 4, ± 5, ± 10 8. Solve by factoring. a) x x 6x = 0 b) x x 5x + 6 = 0 c) x 4 + x 7x 1x 4 = 0 9. Determine an equation for the cubic function represented by this graph. 4. a) Divide x x 1 by x +. Express the result in quotient form. b) Identify any restrictions on the variable. c) Write the corresponding statement that can be used to check the division. 5. a) Determine the value of k such that when P(x) = x 4 x + kx 4 is divided by x +, the remainder is. b) Determine the remainder when P(x) is divided by x 1. c) Verify your answer in part b) using long division. 6. Factor. a) x 15y b) x 4x 9x + 6 c) x + 4x + x 6 d) x + 8x + x e) x 4 4x x + 16x 1 10. Determine an equation, in simplified form, for the family of quartic functions with zeros 1 ± and ± 5. 11. Use Technology Solve. Round answers to one decimal place. a) x 6x + x 6 0 b) x 4 x < 5x x 1. Solve by factoring. a) 4x 64 0 b) x + x + 8x < 0 c) x 4 x x + 7x + 6 > 0 BLM 11 Chapter Test
1. An open-top box is to be constructed from a rectangular piece of cardboard measuring 5 cm by 6 cm. The box is created by cutting congruent corners and then folding up the sides. a) Express the volume of the box as a function of x. b) Use your function from part a) to determine the value(s) of x, to two decimal places, that will result in a volume that is greater than 04 cm. c) Determine the dimensions of the box for the volume given in part b). BLM 11.. (page ) BLM 11 Chapter Test
Chapter Practice Masters Answers BLM 1.. (page 1) Prerequisite Skills 1. a) 17 b) 58 c) 18 54 d) 56. a) x 4 5x 4x + 11x 1 b) x 4 + 10x x 14x 11 c) x 6 d) x 8 e) x +6x + 4. a) (x 7)(x + 7) b) (8a 11b)(8a + 11b) c) (m 5n)(m + 5n) d) 5(x 1)(x + 1)(x + 1) 4. a) (b 5)(b + ) b) (m )(m 6) c) (a + )(a 4) d) (x )(x 5) e) (x + 1)(x 4) 5. a) x = 5 or x = 7 b) x = 5 1 or x = 5 c) x = or x = 5 d) x = 1 or x = 6 1 7 e) x = or x = 5 6. a) x 0. or x 1.4 b) x.9 or x 0.9 c) x 1.1 or x.9 7. a) y = x x 10 b) y = x + 1x c) y = 4x 5x + 0 8. a) i) 1 and ii) above the x-axis: 1 < x < ; below the x-axis: x < 1 or x > b) i), 1, and ii) above the x-axis: x < or 1 < x < ; below the x-axis: < x < 1 or x >.1 The Remainder Theorem 1. a) x 6 7x + 15 + x + b) x c) (x 7x + 15)(x + ) 6 x + x 5x +. a) = x 5 + x + x 4x + x 4 b) = x x + + x + 1 1 x 1 x +, 6, x + 1 4 9x + 6x + 6x 5 c) = x x 1 + +, x x 8x 10x 1 d) = x 8x 105 +14x + 4 +, x x. a) 5 b) 10 4. (x ) cm by (x ) cm by (x 4) cm One possible answer: 7 cm by 7 cm by 1 cm 5. a) 4 b) 50 c) 8 6. a) 5 7. 5 40 8. 4 81 9. a) 1 10. a) 0 b) x(x + 1)(4x 1) 5 11 11. m =, n =. The Factor Theorem 1. a) not a factor b) factor c) factor. a) ± 1, ± ; (x )(x 1)(x + 1) b) ± 1, ±, ±, ± 6; (x + )(x + 1)(x ) c) ± 1, ±, ±, ± 4, ± 6, ± 8, ± 1, ± 4; (x + 4)(x + )(x ). a) (x + )(x )(x + ) b) (x + 5)(x )(x + ) c) (x )(x 5)(x + 5) d) (x 5) (x )(x + ) 4. a) ± 1, ±, ± 4, ± 8; (x 1)(x )(x + 4) b) ± 1, ±, ± 1 ; (x 1)(x + 1)(x + ) 1 c) ± 1, ±, ±, ± 6, ±, (x + 1)(x + )(x ) 1 d) ± 1, ±, ±, ± 6, ±, (x 1)(x )(x ) 5. a) (x + 1)(x 1)(x + 5) b) (x 1)(x )(x + ) c) (x )(x + )(x ) d) (x + 1)(x + )(x )(x + ) e) (x 1)(x )(x + 4)(x 4) ± ; ± ; BLM 1 Chapter Practice Masters Answers
Chapter Practice Masters Answers BLM 1.. (page ) 6. a) (x + 1)(x )(x + ) b) (x + 1)(4x 1)(x ) c) (x 4)(x + )(5x ) 7. 1 8. 6 9. a) (x )(x 5)(x 7) b). m by 5.4 m by.4 m 10. a) (x + )(x 1)(x + 5) b) (x 1)(x + 1)(x + ) c) (5x )(x 1)(x ) d) (4x + 1)(x + )(x ) 11. a) (x 5)(4x + 10x + 5) 8 4 b) 4x + 16x x + 9 c) (6x + y)(6x 6xy + y ) d) ( t )(9 + t + t 4 ) 1 4 5 1 e) 5x y 5x + x y + y 4 4 16 f) (x + 7y 4 )(4x 4 14x y 4 + 49y 8 ) 1. a) (4x 1)(4x +1)(x 1)(x + 1) b) (x 5)(x + 5)(x )(x + ) 1. y = 7 1 (x )(x )(x + 4) 14. (x 1)(x +)(x )(x + 1)(x + 1). Polynomial Equations 1. a) x = 0 or x = 1 or x = b) x = 1 or x = or x = c) x = or x = or x =. a) x = or x = 1 or x = b) x = or x = 1 or x = 5 c) x = 1 or x = 4 1 or x = 1. a) x = or x = 1 or x = b) x = 5 or x = or x = c) x = 4 or x = or x = 0 4. a) x = 1 b) x = 5 or x = 5 c) x = 4 or x = 4 d) x = or x = or x = 1 5. a) 1 b) c),, d) 4,,, 4 6. a) x = or x = 1 or x = b) x = or x = 1 or x = 0 or x = 4 c) x = 0 or x = or x = d) x = 4 or x = 1 or x = e) x = or x = 1 or x = f) x = 5 or x = 1 or x = 1 or x = 5 7. a) x 0.1 b) x 0.68 or x 5.66 c) x 1.47 d) x 1.1 or x 1.51 8..86 m by 7.9 m by 4.86 m 9. 10 cm by 10 cm by 5 cm 15 ± i 111 10. x = 1 or x = 6 11. x 19x + 1x 65 = 0.4 Families of Polynomial Functions 1. a) y = k(x + )(x 5), k, k 0 b) Answers may vary. c) y = 1 (x + )(x 5). D (has different zeros). C (has different zeros) 4. a) y = x(x + )(x ) b) y = 1 x(x + )(x ) c) y = 1 x(x 4)(x + ) 5. A, C, and D (zeros are, 1, 4); B, E, and F (zeros are 4,, 1) 6. a) i) y = k(x + 5)(x )(x 7) ii) y = k(x + 6)(x + )(x ) iii) y = k(x + 4)(x + 1)(x )(x 5) b) i) y = 9 (x + 5)(x )(x 7) 4 ii) y = (x + 6)(x + )(x ) 1 iii) y = 5 1 (x + 4)(x + 1)(x )(x 5) 7. a) y = k(x + )(x )(x 5) b) Answers may vary. c) y = 1 (x + )(x )(x 5) d) Answers may vary. BLM 1 Chapter Practice Masters Answers
Chapter Practice Masters Answers BLM 1.. (page ) 8. a) y = k(x)(x + 4)(x + 1)(x ) b) Answers may vary. c) y = x(x + 4)(x + 1)(x ) d) Answers may vary. 9. a) y = k(x + )(x 1)(x 5) b) y = (x + )(x 1)(x 5) c).5 Solve Inequalities Using Technology 1. a) 4 x b) 6 < x < 1 c) < x 5 d) 1 x <. a) x < 7, 7 < x < 1, x > 1 b) x <, < x < 4, x > 4 c) x <, < x < 0, 0 < x < 6, x > 6. a) intervals where f(x) is above the x-axis b) intervals where f(x) is on or below the x-axis 4. 10. a) y = k(x 10x + 9x 6) b) y = (x 10x + 9x 6) 11. y = (x + )(x 1)(x 4) 4 1. a) y = k (x 4 + 4x 7x x + 4) b) y = (x 4 + 4x 7x x + 4) 1. a) V(x) = x(0 x)(0 x) b) i) V(x) = x(15 x)(0 x) ii) V(x) = x(0 x)(0 x) c) They all have the same zeros. d) e) cm by 4 cm by 4 c m or 7. cm by 15.4 cm by 15.4 cm 14. a) Answers may vary. Sample answer: y = k(x)(x 5)(x + 5) b) y = 8x + 50x c) y = 8x 50x d) It is an odd function, since f( x)= f(x). 5. a) i), 4 ii) < x < 4 iii) x <, x > 4 b) i) 5, ii) x < 5, x > iii) 5 < x < c) i), 1, 5 ii) < x < 1, x > 5 iii) x <, 1 < x < 5 d) i), 1,, 4 ii) < x < 1, < x < 4 iii) x <, 1 < x <, x > 4 6. a) x 4 b) x < 6 or x > 1 c) 4 x 1 or x 4 d) x < or 1 < x < e) x o r x 5 7. a) 0.5 < x < b) x.5 or x 4.5 c) 1 < x < or x > d) x or 1 x e) x or x 5 8. a) x 0. or x.8 b) x < 1.4 or 0. < x < 1.16 c) x < 0.9 d) x.66 or 1.1 x 1.87 e) 0.77 < x < 1.1 9. a) x >.7 b) x < 0.5 c).4 x 0.5 or x.9 d) 1. x.8 10. from 0 s to 0. s and between 6.1 s and 6.54 s 11. Answers may vary. Sample answer: 8x 4 68x + 4x + 45x 55 > 0 1. x 0.68 or x 1.14 BLM 1 Chapter Practice Masters Answers
Chapter Practice Masters Answers BLM 1.. (page 4).6 Solve Factorable Polynomial Inequalities Algebraically 1. a) x > b) x c) x > 4 d) x 1. a) x or x 1 b) < x < 5. a) x < 4 or x > b) x 1 4. a) x 4 or x 6 5 1 b) x or x c) 1 < x < or x > d) 1 < x < or x > 5. a) 5 < x < b) x 7 or x 1 c) x or x 1 d) < x < 1 or x > 6. a) x 1 or x b) x < 1 or < x < 4 c) x < 0 or < x < 1 d) x 1 or 0 x 4 7. a) 4 < x < 6 b) x or x 1 1 c) x < or 1 < x < d) 1 x or x 4 8. 1 cm by 10 cm by cm 9. x 1 or 1 x or x Chapter Review 1. a) i) 1 x 4 1 ii) + x = x + 6x + 1 + x x, x b) i) 54 x 5x + x 6 ii) = x 5 54 x + 10x+ 5+, x 5 x 5 4 x x 4x + 5x 15 c) i) 18 ii) =, x + 1 18 x x x+ + x +, x 1 1. a) 15. 10 4. a) ± 1, ±, ± 4, ± 8; (x 1)(x )(x + 4) b) ± 1, ±, ± 1 ; (x + 1)(x + 1)(x + ) c) ± 1, ±, ± 4, ± 8, ± 1, ± 4, ±, ± 8 ; (x + 1)(x + )(x )(x ) 5. a) (x ) (x + ) b) (x + 1)(x 5)(x + 5) c) (x + )(x )(x + ) 6. 50 1 7. 1 8. a) (x 0) cm by (x 5) cm by (x 8) cm b) 5 cm by 0 cm by 17 cm 9. x = 5 or x = 1 or x = 10. a) 4 b) c) 5,,, 5 11. a) x = or x = 5 b) x = or x = 5 or x = 5 1. a) x 1. b) x 1.46 or x 1.4 or x 4.6 c) x 1. or x 0.8 1. a) V(x) = x(x 6)(1.5x ) b) 0.68 cm by 14.68 cm by 8.0 cm 14. a) y = k(x + 1)(x )(x 6) b) Answers may vary. c) y = (x + 1)(x )(x 6) 15. a) y = k(x + x 11x 15) b) y = (x + x 11x 15) 16. a) x 4. b) x < 1.15 or 0 < x < 1.15 c).81 x 0.76 d) x < 1.0 17. BLM 1 Chapter Practice Masters Answers
Chapter Practice Masters Answers BLM 1.. (page 5) 18. a) x or x 5 4 b) 5 x 1 or x c) x < or < x < or x > 19. a) 5 < x < b) x < or 1 < x < c) 5 x 5 Chapter Test 1. C. C. B x x 1 4. a) = x 7x +14 + x + b) x c) (x 7x +14)(x + ) 9 81 5. a) 19 b) 16 6. a) (x 5y)(x + 5xy + 5y ) b) (x )(x + )(x 4) c) (x 1)(x + ) (x + ) d) (x 1)(x + )(x + 1) e) (x 1)(x + )(x )(x ) 7. x = 4 or x = 1 or x = 1 or x = 8. a) x = or x = 0 or x = b) x = or x = 1 or x = 9 x + c) x = or x = 1 or x = 1 or x = 9. y = (x + 4)(x + 1)(x ) 10. y = x 4 6x + 5x + 10x + 11. a) x. b) 0.5 < x <1. 1. a) x 4 or x 4 b) < x < 0 or x > 4 c) x < 1 or 1 < x < or x > 1. a) V(x) = x(6 x)(5 x) b) 1.96 < x < 1.5 c) 1.96 cm by.08 cm by 48.08 cm or 1.5 cm by 8.96 cm by 4.96 cm BLM 1 Chapter Practice Masters Answers