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Chapter 1: Polynomials Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Divide: A. B. R(–8) R8 C. D. ____ 2. What is the remainder when A. 515 B. –4 ____ 3. Divide by A. B. C. D. =( =( =( =( A. B. )( )( )( )( D. –45 ) ) + 12 ) )–4 , what is the value of C. 27 as a factor? C. D. ____ 6. Factor: A. B. ? . Write the division statement. B. –69 ____ 5. Which polynomial has is divided by C. –3 ____ 4. For the polynomial A. 47 R(–8) R8 C. D. ? D. 59 ____ 7. When A. –13 is divided by B. –5 , the remainder is 1. What is the value of q? C. 15 ____ 8. Which binomial is NOT a factor of A. B. D. 8 ? C. D. ____ 9. The volume of a shipping box with the shapeof a rectangular prism can be expressed as the polynomial . Each dimension of the box can be expressed as a binomial. Which binomial could represent one dimension of the box? A. B. C. D. ____10. Use graphing technology. Graph the polynomial function Which characteristics apply to the graph? A. Number of x-intercepts: 2 Number of hills: 2 Number of valleys: 1 B. Number of x-intercepts: 2 Number of hills: 1 Number of valleys: 1 . C. Number of x-intercepts: 1 Number of hills: 1 Number of valleys: 2 D. Number of x-intercepts: 3 Number of hills: 1 Number of valleys: 1 ____11. Which statements are always true for both the graphs of cubic functions and the graphs of quintic functions? i) The graphs have an odd number of x-intercepts. ii) The graphs never have equal numbers of hills and valleys. iii) The values of the constant terms in the equations are the y-intercepts of the graphs. iv) When the terms with the greatest degree in the equations are negative, the graphs rise to the left and fall to the right. A. iii, iv B. i, ii, iv C. i, iv D. i, ii, iii ____12. Which type of polynomial function is f(x) = 2x5 – 2x3 + 7x2? A. quadratic B. quartic C. cubic D. quintic ____13. The graph of a polynomial function of degree 5 is shown. Which statements are true? i) The function has an even degree. ii) The function has two zeros of multiplicity 2. iii) The equation of the function has a negative leading coefficient. iv) The y-intercept is positive. y 0 A. i, ii, iv x B. i, ii, iii C. ii, iii, iv D. i, iii, iv ____14. Determine the zeros of the polynomial function multiplicity of each zero. A. B. C. D. The zero –5 has multiplicity 3; the zero –4 has multiplicity 2. The zero 5 has multiplicity 3; the zero 4 has multiplicity 2. The zero 3 has multiplicity 5; the zero 2 has multiplicity 4. The zero 3 has multiplicity –5; the zero 2 has multiplicity –4. . State the ____15. Identify the graph that corresponds to the function y A. C. 32 64 16 32 –8 –6 –4 –2 0 B. . y 2 4 6 8 –8 –6 –4 –2 x –16 –32 –32 –64 y D. 32 16 –8 –6 –4 –2 0 2 4 6 8 x 2 4 6 8 x y 32 16 2 4 6 8 –8 –6 –4 –2 x –16 –16 –32 –32 ____16. A carton of juice in the shape of a rectangular prism has dimensions 5.4 cm by 5.4 cm by 9.2 cm. The manufacturer wants to design a carton with double the capacity by increasing each dimension by x centimetres. Which equation could be used to determine the value of x? A. B. C. D. Short Answer 1. When is divided by Write the division statement. using synthetic division, the result is: 2. Determine the quotient and remainder when the polynomial divided by . 3. Determine one binomial factor of is . 4. Graph the polynomial function Complete the table for the graph. using graphing technology. Number Number of Number yof x-intercepts of hills intercept valleys 5. Identify each polynomial function as a quadratic, cubic, quartic, or quintic function. a) b) c) d) 6. Write an equation in standard form for a cubic function with zeros –1, –3, and –4 and a y-intercept of 6 7. A rectangular prism has dimensions x centimetres, centimetres, and centimetres. Determine the maximum volume of the prism to the nearest tenth of a cubic centimetre. Problem 1. Is a factor of ? How do you know? 2. A quartic function has these characteristics: leading coefficient is negative; zero 2 has multiplicity 2, each of the zeros 1 and 3 has multiplicity 1. Sketch a possible graph of the function. Justify your thinking. Label the graph with its equation and label the y-intercept. 3. A cubic function has zeros 2, –1, and –3. The y-intercept of its graph is –12. Sketch the graph, then determine an equation of the function in standard form. Explain your work. 4. A rectangular prism has width x units, length units, and height Suppose the prism has volume . Determine its dimensions. units. Chapter 1: Polynomials Practice Test Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 0 DIF: REF: 1.1 Dividing a Polynomial by a Binomial TOP: Relations and Functions KEY: Procedural Knowledge Moderate LOC: 12.RF11 Conceptual Understanding | 2. ANS: A PTS: 0 DIF: REF: 1.1 Dividing a Polynomial by a Binomial TOP: Relations and Functions KEY: Procedural Knowledge Moderate LOC: 12.RF11 Conceptual Understanding | 3. ANS: B PTS: 0 DIF: REF: 1.1 Dividing a Polynomial by a Binomial TOP: Relations and Functions KEY: Procedural Knowledge Moderate LOC: 12.RF11 Conceptual Understanding | 4. ANS: Polynomials LOC: KEY: C Easy REF: 1.2 Factoring 5. ANS: Polynomials LOC: KEY: C 6. ANS: Polynomials LOC: KEY: C 7. ANS: Polynomials LOC: KEY: A PTS: 0 DIF: 12.RF11 TOP: Relations and Functions Conceptual Understanding | Procedural Knowledge PTS: 0 DIF: Easy REF: 1.2 Factoring 12.RF11 TOP: Relations and Functions Conceptual Understanding | Procedural Knowledge PTS: 0 DIF: Difficult REF: 1.2 Factoring 12.RF11 TOP: Relations and Functions Conceptual Understanding | Procedural Knowledge PTS: 0 DIF: Moderate REF: 1.2 Factoring 12.RF11 TOP: Relations and Functions Conceptual Understanding | Problem-Solving Skills 8. ANS: Polynomials LOC: KEY: A 9. ANS: Polynomials LOC: KEY: A PTS: 0 DIF: Moderate REF: 1.2 Factoring 12.RF11 TOP: Relations and Functions Conceptual Understanding | Procedural Knowledge PTS: 0 DIF: Difficult REF: 1.2 Factoring 12.RF11 TOP: Relations and Functions Procedural Knowledge | Problem-Solving Skills 10. ANS: B PTS: 0 DIF: Easy REF: 1.3 Graphing Polynomial Functions LOC: 12.RF12 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge 11. ANS: A PTS: Polynomial Functions LOC: 12.RF12 Conceptual Understanding 0 DIF: Moderate REF: 1.3 Graphing TOP: Relations and Functions KEY: 12. ANS: D PTS: 0 DIF: Easy REF: 1.4 Relating Polynomial Functions and Equations LOC: 12.RF12 TOP: Relations and Functions KEY: Conceptual Understanding 13. ANS: C PTS: 0 DIF: Moderate REF: 1.4 Relating Polynomial Functions and Equations LOC: 12.RF12 TOP: Relations and Functions KEY: Conceptual Understanding 14. ANS: A PTS: 0 DIF: Easy REF: 1.4 Relating Polynomial Functions and Equations LOC: 12.RF12 TOP: Relations and Functions KEY: Conceptual Understanding 15. ANS: D PTS: 0 DIF: Moderate REF: 1.4 Relating Polynomial Functions and Equations LOC: 12.RF12 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge 16. ANS: C PTS: 0 DIF: Moderate REF: 1.5 Modelling and Solving Problems with Polynomial Functions LOC: KEY: 12.RF12 TOP: Relations and Functions Procedural Knowledge | Problem-Solving Skills SHORT ANSWER 1. ANS: PTS: 0 LOC: KEY: DIF: Easy REF: 1.1 Dividing a Polynomial by a Binomial 12.RF11 TOP: Relations and Functions Conceptual Understanding | Procedural Knowledge 2. ANS: R(–4) PTS: 0 LOC: KEY: 3. ANS: , PTS: 0 LOC: KEY: DIF: Moderate REF: 1.1 Dividing a Polynomial by a Binomial 12.RF11 TOP: Relations and Functions Conceptual Understanding | Procedural Knowledge , or DIF: Moderate REF: 1.2 Factoring Polynomials 12.RF11 TOP: Relations and Functions Conceptual Understanding | Procedural Knowledge 4. ANS: Number Number of Number yof x-intercepts of hills intercept valleys 3 1 1 5 PTS: 0 LOC: KEY: DIF: Easy REF: 1.3 Graphing Polynomial Functions 12.RF12 TOP: Relations and Functions Procedural Knowledge | Communication 5. ANS: a) cubic function b) quintic function c) quadratic function d) quartic function PTS: 0 DIF: Easy Equations LOC: 12.RF12 Conceptual Understanding REF: 1.4 Relating Polynomial Functions and TOP: Relations and Functions KEY: 6. ANS: Answers may vary by a common numerical factor. For example: PTS: 0 Equations LOC: KEY: DIF: Moderate REF: 1.4 Relating Polynomial Functions and 12.RF12 TOP: Relations and Functions Procedural Knowledge | Communication 7. ANS: PTS: 0 DIF: Moderate REF: 1.5 Modelling and Solving Problems with Polynomial Functions LOC: 12.RF12 TOP: Relations and Functions KEY: Procedural Knowledge | Problem-Solving Skills PROBLEM 1. ANS: Let is a factor of Since P(2) is 0, PTS: 0 LOC: KEY: . if . is a factor of . DIF: Easy REF: 1.2 Factoring Polynomials 12.RF11 TOP: Relations and Functions Procedural Knowledge | Communication 2. ANS: The zero 2 has multiplicity 2, so the graph just touches the x-axis at . Each of the zeros 1 and 3 has multiplicity 1, so the graph crosses the x-axis at and . Since the function is quartic, there are no more zeros. The leading coefficient is negative, so as , the graph falls to the left, and as , the graph falls to the right. That is, the graph opens down. A possible graph is: y –3 –1 0 2 x –12 A possible equation is: The y-intercept for this function is: PTS: 0 Equations LOC: KEY: DIF: Moderate REF: 1.4 Relating Polynomial Functions and 12.RF12 TOP: Relations and Functions Conceptual Understanding | Communication 3. ANS: Sketch the graph: y –3 –10 2 x –12 The zeros of the function are the roots of its related polynomial equation. Let k represent the leading coefficient. The constant term in the equation is –12. So, So, an equation is: PTS: 0 Equations LOC: KEY: DIF: Moderate REF: 1.4 Relating Polynomial Functions and 12.RF12 TOP: Relations and Functions Procedural Knowledge | Communication 4. ANS: The prism has dimensions 9 units by 16 units by 26 units. PTS: 0 DIF: Moderate REF: 1.5 Modelling and Solving Problems with Polynomial Functions LOC: 12.RF12 TOP: Relations and Functions KEY: Procedural Knowledge | Problem-Solving Skills