Controlling the Population

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1 Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1 term 2. term b. the degree of the term with the greatest exponent 3. coefficient c. a mathematical expression involving the sum of powers in one or more variables multiplied by coefficients 4. monomial d. a polynomial with exactly 3 terms 5. binomial e. any number being multiplied by a power within a polynomial expression 6. trinomial f. each product in a polynomial expression 7. degree of a term g. a polynomial with exactly 2 terms 8. degree of a polynomial h. the exponent of a term in a polynomial Chapter Skills Practice 915

2 Lesson.1 Skills Practice page 2 Problem Set Identify the terms and coefficients in each expression. 1. 5x 1 8 The terms are 5x and 8. The coefficients are 5 and m 3 3. x 2 2 4x 4. 23w 4 1 w x 3 2 6x Determine whether each expression is a polynomial. If the expression is not a polynomial, explain why it is not x The expression is a polynomial. 8. 6m x 2 8x w3 1 w m 12. x x m Chapter Skills Practice

3 Lesson.1 Skills Practice page 3 Name Date Determine whether each polynomial is a monomial, binomial, or trinomial. State the degree of the polynomial x 1 3 The polynomial is a binomial with a degree of m x 2 2 7x n 4 1 6n x 3 1 8x Write each polynomial in standard form. Classify the polynomial by its number of terms and by its degree x 1 6x 2 6x 2 1 2x The polynomial is a binomial with a degree of m 2 1 4m x 24. 7x x w 2 w x x p t 2 1 4t 1 3t 3 Chapter Skills Practice 917

4 Lesson.1 Skills Practice page a a 2 22a x 3 2 x 2 2 x 5 Simplify each expression. 31. (5x 2 8) 1 (7x 110) 5x x 1 10 (5x 1 7x) 1 ( ) 12x (4m 2 1 9m) 2 (2m 2 1 6) 33. (2x 2 1 5x 2 12) 1 (2x 2 2 6) 34. (10t 2 2 3t 1 9) 2 (6t 2 2 7t) 35. (25w 2 1 3w 2 8) 1 (15w 2 2 4w 1 11) 36. (3x x 2 1) 2 (5x x 2 9) 37. (2a 2 1 2a 2 8) 1 (2a 2 2 9a 1 15) 38. (14p 4 1 7p 2 ) 1 (8p 3 1 7p 2 2 p) 39. (3x x 2 2 3) 2 (6 x x 3 1 2) 40. (27m 3 2 m 2 2 m) 2 (210m 3 2 m 2 1) 918 Chapter Skills Practice

5 Lesson.1 Skills Practice page 5 Name Date The graphs of the functions f(x) 5 2x 1 1, g(x) 5 x 2 1 x 2 3, and h(x) 5 f(x) 1 g(x) are shown. Evaluate the function h(x) for each given value of x. Use the graph of h(x) to verify your answer. g(x) y h(x) x f(x) Evaluate h(x) at x 5 2. h(x) 5 f(x) 1 g(x) 5 2x x 2 1 x x 2 1 3x 2 2 h(2) 5 (2 ) 2 1 3(2) Evaluate h(x) at x Evaluate h(x) at x Evaluate h(x) at x 5 1. Chapter Skills Practice 919

6 Lesson.1 Skills Practice page Evaluate h(x) at x Evaluate h(x) at x Chapter Skills Practice

7 Lesson.2 Skills Practice Name Date They re Multiplying Like Polynomials! Multiplying Polynomials Problem Set Determine the product of the binomials using algebra tiles. 1. x 1 1 and x x 1 1 and x 1 4 x 1 x x 2 x 1 x 1 (x 1 1) (x 1 1) 5 x 2 1 2x x 1 2 and x x 1 3 and x 1 3 Chapter Skills Practice 921

8 Lesson.2 Skills Practice page x 1 1 and x x 1 3 and x 1 2 Determine the product of the binomials using multiplication tables. 7. 3x 1 4 and 2x m 1 3 and 4m 1 6? 2x 2 3x 6x 2 6x 4 8x 8 (3x 1 4)(2x 1 2) 5 6 x 2 1 6x 1 8x x x t 1 5 and 7t x 1 2 and 4x Chapter Skills Practice

9 Lesson.2 Skills Practice page 3 Name Date w 2 1 and 9w y 1 12 and 5y 1 15 Determine the product of the polynomials using the Distributive Property.. 2x(x 1 6) 2x(x 1 6) 5 2x(x) 1 2x(6) 5 2 x x x 2 (x 1 2) 15. 7x(x 2 5) 16. (2x 1 1)(x 1 8) 17. (x 1 3)( x 2 2 1) 18. (4x 1 4)(5x 2 5) 19. 3x( x 2 1 5x 2 1) 20. 9x(3 x 2 2 4x 1 2) Chapter Skills Practice 923

10 Lesson.2 Skills Practice page (x 1 2)( x 2 1 6x 2 1) 22. (x 2 4)( x 2 1 2x 2 3) 924 Chapter Skills Practice

11 Lesson.3 Skills Practice Name Date What Factored Into It? Factoring Polynomials Vocabulary State the given property. 1. Symmetric Property of Equality Problem Set Factor out the greatest common factor of each polynomial, if possible. 1. x 2 1 9x x(x 1 9) 2. m 2 2 4m 3. 5 x x w y 3 2 7y 6. 2 x x w x x 2 1 8x 9. 7 m x Chapter Skills Practice 925

12 Lesson.3 Skills Practice page 2 Factor each trinomial using an area model. 11. x 2 1 4x 1 3 x 1 3 x x 1 1 x x 2 x x x 1 x x 2 1 4x (x 1 1)(x 1 3) 12. x 2 1 5x 1 6. x 2 2 x Chapter Skills Practice

13 Lesson.3 Skills Practice page 3 Name Date 14. x 2 2 x x 2 1 7x x 2 1 3x 2 4 Chapter Skills Practice 927

14 Lesson.3 Skills Practice page 4 Factor each trinomial completely using multiplication tables. If possible, factor out the greatest common factor first. 17. x 2 2 2x y 2 1 y 1 42? x 2 x x 2 2x 24 24x 28 x 2 2 2x (x 2 4)(x 1 2) 19. m 2 1 6m x 2 2 9x w w t t t m m m x 2 2 8x Chapter Skills Practice

15 Lesson.3 Skills Practice page 5 Name Date Factor each polynomial using the trial and error method. If possible, factor out the greatest common factor first. 25. x x 1 10 The factors of the constant term, 10, are: 21, 210 1, 10 22, 25 2, 5 x x (x 1 1)(x 1 10) 26. w 2 1 6w m 2 1 2m x 2 1 4x n n x x 1 60 Factor each polynomial. 31. x x (x 1 4)(x 1 7) x x (x 2 4)(x 2 7) x 2 1 3x (x 2 4)(x 1 7) x 2 2 3x (x 1 4)(x 2 7) 32. x x x x x 2 1 8x x 2 2 8x x x x 2 1 x x x x 2 2 x x 2 1 6x x 2 1 3x x 2 2 6x x 2 2 3x Chapter Skills Practice 929

16 Lesson.3 Skills Practice page x x x x x x x x x 2 1 x x 2 2 x x 2 1 5x x 2 2 5x Factor each polynomial completely. If possible, factor out the greatest common factor first. 37. x 2 1 4x x x 1 25? x 2 x x 2 2x 2 2x 4 x 2 1 4x (x 1 2)(x 1 2) m 2 m w 2 w x x x x Chapter Skills Practice

17 Lesson.4 Skills Practice Name Date Zeroing In Solving Quadratics by Factoring Vocabulary Complete the definition of the Zero Product Property. 1. The Zero Product Property states that if the product of two or more factors is equal to, then at least one factor must be equal to. If ab 5 0, then or. This property is also known as the. Define the term in your own words. 2. roots Problem Set Factor and solve each quadratic equation. Check your answer. 1. x 2 1 5x x 2 1 5x Check: (x 1 3)(x 1 2) 5 0 (2 3) 2 1 5(23) (2 2) 2 1 5(22) x or x x 5 23 or x The roots are 23 and x 2 2 3x Chapter Skills Practice 931

18 Lesson.4 Skills Practice page 2 3. m 2 1 2m x 2 2 4x x 2 1 8x w w 7. 2 t t Chapter Skills Practice

19 Lesson.4 Skills Practice page 3 Name Date 8. x 2 1 2x t 2 1 t w 2 1 5w w 2 4 Chapter Skills Practice 933

20 Lesson.4 Skills Practice page 4 Determine the zeros of each quadratic function, if possible. Check your answer. 11. f(x) 5 x 2 2 5x f(x) 5 x 2 2 5x Check: 0 5 x 2 2 5x (0 ) 2 2 5(0) 0 0 (5 ) 2 2 5(5) x(x 2 5) x 5 0 or x x 5 0 or x 5 5 The zeros are 0 and f(x) 5 3 x 2 1 6x. f(x) 5 x x f(x) 5 x 2 2 9x Chapter Skills Practice

21 Lesson.4 Skills Practice page 5 Name Date 15. f(x) 5 2 x 2 1 9x f(x) 5 x 2 1 5x f(x) 5 3 x 2 1 3x 2 6 Chapter Skills Practice 935

22 Lesson.4 Skills Practice page f(x) x x 936 Chapter Skills Practice

23 Lesson.5 Skills Practice Name Date What Makes You So Special? Special Products Vocabulary Give an example of each term. Then, factor the expression. 1. perfect square trinomial 2. difference of two squares 3. sum of two cubes 4. difference of two cubes Problem Set Factor each binomial completely. 1. x x (x 1 5)(x 2 5) 2. x x m Chapter Skills Practice 937

24 Lesson.5 Skills Practice page x t a x 8 2 y 8 Factor the trinomial completely. 9. x x 1 64 x x (x 1 8)(x 1 8) 10. k k x x x x 1 5. z z z 14. 3x x x Determine the root(s) of each quadratic equation. Check your answer(s). 15. x x Check: (x 1 10)(x 2 10) 5 0 (2 10) ( 10) x or x x or x The roots are 210 and m m Chapter Skills Practice

25 Lesson.5 Skills Practice page 3 Name Date x x x t t w w Chapter Skills Practice 939

26 Lesson.5 Skills Practice page 4 Determine the zero(s) of each quadratic function. Check your answer(s). 21. f(x) 5 x f(x) 5 x Check: 0 5 x (215 ) (15 ) (x 1 15)(x 2 15) x or x x or x 5 15 The zeros are 215 and f(x) 5 x 2 1 x f(x) 5 9 x Chapter Skills Practice

27 Lesson.5 Skills Practice page 5 Name Date 24. f(x) 5 8 x x f(x) 5 8 x f(x) 5 2 x x Chapter Skills Practice 941

28 942 Chapter Skills Practice

29 Lesson.6 Skills Practice Name Date Could It Be Groovy to Be a Square? Approximating and Rewriting Radicals Vocabulary Choose the word that best completes each statement. square root positive (principal) square root radicand negative square root extract the square root radical expression 1. When solving certain quadratic equations, it is necessary to from both sides of the equation. 2. Every positive number has both a(n) and a(n). 3. The is the expression enclosed within a radical symbol. 4. A number b is a(n) of a if b 2 5 a. 5. An expression involving a radical symbol is called a(n). Problem Set Rewrite each radical by extracting all perfect squares Chapter Skills Practice 943

30 Lesson.6 Skills Practice page Determine the approximate value of each radical expression to the nearest tenth < Solve each quadratic equation. Approximate the roots to the nearest tenth. 15. x x x x < 66.3 x < 66.3 The roots are approximately 6.3 and m Chapter Skills Practice

31 Lesson.6 Skills Practice page 3 Name Date 17. t x (x 2 5) (x 1 8) Solve each quadratic equation. Rewrite the roots in radical form. 21. x x x x x ? 3 x ? 3 x The roots are 4 3 and x Chapter Skills Practice 945

32 Lesson.6 Skills Practice page x x (12 2 x) (x 1 20) Chapter Skills Practice

33 Lesson.7 Skills Practice Name Date Another Method Completing the Square Vocabulary Define the term in your own words. 1. completing the square Problem Set Use a geometric figure to complete the square for each expression. Factor the resulting trinomial. 1. x 2 1 2x 2. x 2 1 4x 1 x 1 x x 2 x x 1 x 2 1 2x (x 1 1) 2 3. x x 4. x 2 1 9x Chapter Skills Practice 947

34 Lesson.7 Skills Practice page 2 5. x x 6. x x Determine the unknown value that would make each trinomial a perfect square. 7. x x x x 1 9. x 2 1 x x 2 2 x x 2 1 7x x x 1. x 2 2 x x 2 1 x Determine the roots of each quadratic equation by completing the square. Round your answer to the nearest hundredth. Check your answer. 15. x 2 1 4x x 2 1 4x Check: x 2 1 4x 5 6 (1.16) 2 1 4(1.16) (25.16) 2 2 4(25.16) x 2 1 4x (x 1 2) (x 1 2) x x x < 1.16 or x < < < 0 The roots are approximately 1.16 and Chapter Skills Practice

35 Lesson.7 Skills Practice page 3 Name Date 16. x 2 2 2x x x x x Chapter Skills Practice 949

36 Lesson.7 Skills Practice page x 2 1 3x x 2 1 x Chapter Skills Practice

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