Controlling the Population
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- Ruth Wilkerson
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1 Lesson. Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term.. polynomial c. a. a polynomial with only term. term f. b. the degree of the term with the greatest eponent 3. coefficient e. c. a mathematical epression involving the sum of powers in one or more variables multiplied by coefficients 4. monomial a. d. a polynomial with eactly 3 terms 5. binomial g. e. any number being multiplied by a power within a polynomial epression 6. trinomial d. 7. degree of a term h. 8. degree of a polynomial b. f. each product in a polynomial epression g. a polynomial with eactly terms h. the eponent of a term in a polynomial Chapter Skills Practice 67
2 Lesson. Skills Practice page Problem Set Identify the terms and coefficients in each epression The terms are 5 and 8. The coefficients are 5 and 8.. m 3 The term is m 3. The coefficient is The terms are and 4. The coefficients are and w 4 w 9 The terms are 3w 4, w, and 9. The coefficients are 3,, and The term is 8. The coefficient is The terms are 0, 3 3, and 6. The coefficients are 0, 3, and 6. Determine whether each epression is a polynomial. If the epression is not a polynomial, eplain why it is not The epression is a polynomial. 8. 6m The epression is not a polynomial, because the term has an eponent that is not a whole number The epression is not a polynomial. The first term can be rewritten as 3 which has an eponent that is not a whole number. 0. w 3 w 5 The epression is a polynomial...5m The epression is a polynomial The epression is not a polynomial. The first term can be rewritten as /3 which has an eponent that is not a whole number The epression is a polynomial m 5 The epression is a polynomial. 68 Chapter Skills Practice
3 Lesson. Skills Practice page 3 Name Date Determine whether each polynomial is a monomial, binomial, or trinomial. State the degree of the polynomial The polynomial is a binomial with a degree of. 6. 5m The polynomial is a monomial with a degree of The polynomial is a binomial with a degree of. 8. 9n 4 6n The polynomial is a trinomial with a degree of The polynomial is a monomial with a degree of The polynomial is a trinomial with a degree of 3. Write each polynomial in standard form. Classify the polynomial by its number of terms and by its degree The polynomial is a binomial with a degree of.. 9m 4m 3 4m 3 9m The polynomial is a binomial with a degree of The polynomial is a binomial with a degree of The polynomial is a trinomial with a degree of w w 3 w 3 4w 5 The polynomial is a trinomial with a degree of p 4 p 4 The polynomial is a binomial with a degree of The polynomial is a trinomial with a degree of. 8. 6t 4t 3t 3 3t 3 6t 4t The polynomial is a trinomial with a degree of 3. Chapter Skills Practice 69
4 Lesson. Skills Practice page a 3 54a a 8a 3 a 54a The polynomial is a trinomial with a degree of The polynomial is a trinomial with a degree of 5. Simplify each epression. 3. (5 8) (7 0) (5 7) (8 0) 3. (4m 9m) (m 6) 4m 9m m 6 (4m m ) 9m 6 m 9m ( 5 ) ( 6) 5 6 ( ) 5 ( 6) (0t 3t 9) (6t 7t) 0t 3t 9 6t 7t (0t 6t ) (3t 7t) 9 4t 4t (5w 3w 8) (5w 4w ) 5w 3w 8 5w 4w (5w 5w ) (3w 4w) (8 ) 0w w (3 3 0 ) (5 0 9) (0 0) ( 9) (a a 8) (a 9a 5) a a 8 a 9a 5 (a a ) (a 9a) (8 5) a 7a ( ) ( ) (3 ) (4p 4 7p ) (8p 3 7p p) 4p 4 7p 8p 3 7p p 4p 4 8p 3 (7p 7p ) p 4p 4 8p 3 p 40. (7m 3 m m) (0m 3 m ) 7m 3 m m 0m 3 m (7m 3 0m 3 ) m (m m) 3m 3 m 60 Chapter Skills Practice
5 Lesson. Skills Practice page 5 Name Date The graphs of the functions f() 5, g() 5 3, and h() 5 f() g() are shown. Evaluate the function h() for each given value of. Use the graph of h() to verify your answer. g() y h() f() 8 4. Evaluate h() at 5. h() 5 f() g() h() 5 ( ) 3() Evaluate h() at 5 4. h() 5 f() g() h(4) 5 (4 ) 3(4) Evaluate h() at 5 0. h() 5 f() g() h(0) 5 (0 ) 3(0) Evaluate h() at 5. h() 5 f() g() h() 5 ( ) 3() Chapter Skills Practice 6
6 Lesson. Skills Practice page Evaluate h() at 5. h() 5 f() g() h() 5 ( ) 3() Evaluate h() at 5.5. h() 5 f() g() h(.5) 5 (.5 ) 3(.5) Chapter Skills Practice
7 Lesson. Skills Practice Name Date They re Multiplying Like Polynomials! Multiplying Polynomials Problem Set Determine the product of the binomials using algebra tiles.. and. and 4 ( ) ( ) 5 ( ) ( 4) and 4. 3 and 3 ( ) ( ) ( 3) ( 3) Chapter Skills Practice 63
8 Lesson. Skills Practice page 5. and and ( )( 3) ( 3)( ) Determine the product of the binomials using multiplication tables and 8. 5m 3 and 4m 6? (3 4)( ) ? 4m 6 5m 0m 30m 3 m 8 (5m 3)(4m 6) 5 0 m 30m m m 4m t 5 and 7t 5? 7t 5 6t 4t 30t 5 35t and 4? (6t 5)(7t 5) 5 4 t 30t 35t t 5t 5 (4 )(4 ) Chapter Skills Practice
9 Lesson. Skills Practice page 3 Name Date. 0w and 9w 8. y and 5y 5? 9w 8 0w 90w 80w 9w 8 (0w )(9w 8) 5 90 w 80w 9w w 7w 8? 5y 5 y 5y 5y 60y 80 (y )(5y 5) 5 5 y 5y 60y y 75y 80 Determine the product of the polynomials using the Distributive Property. 3. ( 6) ( 6) 5 () (6) ( ) 4 ( ) 5 4 () 4 () ( 5) 7( 5) 5 7() 7(5) ( )( 8) ( )( 8) 5 ( )() ( )(8) 5 () () (8) (8) ( 3)( ) ( 3)( ) 5 ( 3)( ) ( 3)() 5 ( ) 3( ) () 3() ( 5 ) 3( 5 ) 5 3( ) 3(5) 3() (4 4)(5 5) (4 4)(5 5) 5 (4 4)(5) (4 4) (5) 5 4(5) 4(5) 4(5) 4(5) (3 4 ) 9(3 4 ) 5 9(3 ) 9(4) 9() Chapter Skills Practice 65
10 Lesson. Skills Practice page 4. ( )( 6 ) ( )( 6 ) 5 ( )( ) ( )(6) ( )() 5 ( ) ( ) (6) (6) () () ( 4)( 3) ( 4)( 3) 5 ( 4)( ) ( 4)() ( 4)(3) 5 ( ) 4( ) () 4() (3) (4)(3) () Chapter Skills Practice
11 Lesson.3 Skills Practice Name Date What Factored Into It? Factoring Polynomials Vocabulary State the given property.. Symmetric Property of Equality The Symmetric Property of Equality states that if m 5 n, then n 5 m. Problem Set Factor out the greatest common factor of each polynomial, if possible.. 9 ( 9). m 4m m(m 4) ( 4 3) 4. 4 w 6 8(3 w ) 5. y 3 7y y( y 7) ( 5) 7. 3w 0 There is no greatest common factor m 3 7( m 3 3) (5 4 ) There is no greatest common factor. Chapter Skills Practice 67
12 Lesson.3 Skills Practice page Factor each trinomial using an area model ( )( 3) ( )( 3) ( )( 3) 68 Chapter Skills Practice
13 Lesson.3 Skills Practice page 3 Name Date ( 3)( 4) ( )( 5) ( )( 4) Chapter Skills Practice 69
14 Lesson.3 Skills Practice page 4 Factor each trinomial completely using multiplication tables. If possible, factor out the greatest common factor first y 3y 4?? y 7 y y 7y y ( 4)( ) y 3y 4 5 ( y 6)( y 7) 9. m 6m ? m? 6 m m m 6 7 7m m 6m 7 5 (m 7)(m ) ( 3)( 6). 4 w w 40. t 3 4 t 4t 4 w w ( w 3w 0) t 3 4 t 4t 5 t( t 7t ) Factor w 3w 0 using a multiplication table. Factor t 7t using a multiplication table.? w w w w 5 5w 0 4 w w (w 5)(w ) 3. 3 m 3 36 m 60m 3 m 3 36 m 60m 5 3m( m m 0) Factor m m 0 using a multiplication table.? t 4 t t 4t 3 3t t 3 4 t 4t 5 t(t 3)(t 4) ( 4 ) Factor 4 using a multiplication table.? m? 7 m m m 7 0 0m m 3 36 m 60m 5 3m(m 0)(m ) ( 3)( 7) 630 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 The factors of the constant term, 0, are:, 0, 0, 5, ( )( 0) 7. m m 35 The factors of the constant term, 35, are:, 35, 35 5, 7 5, 7 m m 35 5 (m 7)(m 5) 9. 3 n 7n 60 3 n 7n ( n 9n 0) Factor n 9n 0 using trial and error. The factors of the constant term, 0, are:, 0, 0, 0, 0 4, 5 4, 5 3 n 7n (n 5)(n 4) 6. w 6w 6 The factors of the constant term, 6, are:, 6, 6, 8, 8 4, 4 4, 4 w 6w 6 5 (w 8)(w ) 8. 4 The factors of the constant term,, are:,,, 6, 6 3, 4 3, ( 6)( ) ( 30) Factor 30 using trial and error. The factors of the constant term, 30, are:, 30, 30, 5, 5 3, 0 3, 0 5, 6 5, ( 5)( 6) Factor each polynomial ( 4)( 7) 8 5 ( 4)( 7) ( 4)( 7) ( 4)( 7) ( )( 9) ( )( 9) ( )( 9) ( )( 9) ( 3)( 9) 7 5 ( 3)( 9) ( 3)( 9) ( 3)( 9) ( 5)( 8) ( 5)( 8) ( 5)( 8) ( 5)( 8) Chapter Skills Practice 63
16 Lesson.3 Skills Practice page ( )( ) 5 ( )( ) 0 5 ( )( ) 0 5 ( )( ) ( 4)( 9) ( 4)( 9) ( 4)( 9) ( 4)( 9) Factor each polynomial completely. If possible, factor out the greatest common factor first ? ( )( )? ( 5)( 5) m m 3 m m 5 ( m m 3) Factor m m 3 using a multiplication table w w 45 4w w 5 ( w 4w 45) Factor w 4w 45 using a multiplication table.? m 8 m m 8m 4 4m 3 3 m m 5 (m 4)(m 8)? w 9 w w 9w 5 5w w w 5 (w 5)(w 9) ( 3) Factor 3 using a multiplication table.? ( 3)( ) ( 8 6) Factor 8 6 using a multiplication table.? ( 4)( 4) 63 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.. The Zero Product Property states that if the product of two or more factors is equal to zero, then at least one factor must be equal to zero. If ab 5 0, then a 5 0 or b 5 0. This property is also known as the Converse of the Multiplication Property of Zero. Define the term in your own words.. roots The solutions to a quadratic equation are called the roots. The roots indicate where the graph of a quadratic equation crosses the -ais. Problem Set Factor and solve each quadratic equation. Check your answer ( 3)( ) 5 0 ( 3) 5(3) ( ) 5() or or The roots are 3 and ( 4)( ) 5 0 ( 4) 3(4) ( ) 3() or or The roots are 4 and. Chapter Skills Practice 633
18 Lesson.4 Skills Practice page 3. m m m m (m 7)(m 5) 5 0 ( 7) (7) ( 5) (5) m or m m 5 7 or m The roots are 7 and ( 4 ) 5 0 ( ) 4() 5 0 ( 6) 4(6) 5 0 ( )( 6) or or 5 6 The roots are and ( 8) 5 0 ( 0) 8(0) 5 0 ( 8) 8(8) or or The roots are 0 and w w w w w 50 5w 5 5w 5w ( 0) (0) ( 5) (5) w 5w (w 0)(w 5) w or w w 5 0 or w 5 5 The roots are 0 and t t 5 3 t t 5 3 t t ( 4) (4) 5 3 ( 8) (8) 5 3 t t ( t t 3) (t 4)(t 8) 5 0 t or t t 5 4 or t 5 8 The roots are 4 and Chapter Skills Practice
19 Lesson.4 Skills Practice page 3 Name Date The equation has no real roots. 9. t t t t (t 3)(t ) 5 0 ( 3 ) ( 3 t or t 5 0 ( 9 4 ) 3 3 t 5 3 ) ( ) () () or 3 t The roots are and w 5w 3 5 w 4 w 5w 3 5 w 4 w 5w 3 w 4 5 w 4 w 4 (7 ) 5(7) 3 5 (7) 4 w 3w (w 7)(w 4) w or w (4 ) 5(4) 3 5 (4) 4 w 5 7 or w The roots are 7 and 4. Chapter Skills Practice 635
20 Lesson.4 Skills Practice page 4 Determine the zeros of each quadratic function, if possible. Check your answer.. f() 5 5 f() (0 ) 5(0) 0 0 (5 ) 5(5) ( 5) or or 5 5 The zeros are 0 and 5.. f() f() (0 ) 6(0) 0 0 3( ) 6() ( ) 3(0) (4) or or The zeros are 0 and. 3. f() 5 30 f() (6 ) (6) (5 ) (5) ( 6)( 5) or or 5 5 The zeros are 6 and f() f() ( ) 9() (3 ) 9(3) ( )( 3) or or 5 3 The zeros are and Chapter Skills Practice
21 Lesson.4 Skills Practice page 5 Name Date 5. f() f() ( 5 ) 9 ( 5 0 5( 5)( ) ( 5 4 ) or ) ( ) 9() (4) or The zeros are and f() The function has no real zeros. 7. f() f() ( ) 3() ( ) 3() ( ) 3(4) () ( )( ) or or 5 The zeros are and. Chapter Skills Practice 637
22 Lesson.4 Skills Practice page 6 8. f() f() (0 ) 4 (0) 0 0 4(0) 5 4 ( 3 4 ) (0) ( 3 ) 3 4 ( 3 ( 9 4 ) ) ( 3) or or The zeros are 0 and. 638 Chapter Skills Practice
23 Lesson.5 Skills Practice Name Date What Makes You So Special? Special Products Vocabulary Give an eample of each term. Then, factor the epression.. perfect square trinomial Answers will vary. The trinomial 36 is an eample of a perfect square trinomial ( 6)( 6). difference of two squares Answers will vary. The binomial 400 is an eample of the difference of two squares ( 0)( 0) 3. sum of two cubes Answers will vary. The binomial 3 is an eample of the sum of two cubes. 3 5 ( )( ) 4. difference of two cubes Answers will vary. The binomial 3 is an eample of the difference of two cubes. 3 5 ( )( ) Problem Set Factor each binomial completely ( 5)( 5) ( 4)( 4 6) ( 3)( 3 9) 4. m 00 m 00 5 (m 0)(m 0) Chapter Skills Practice 639
24 Lesson.5 Skills Practice page ( 3 8) 5 5( )( 4) 7. 8 a 3 7 8a (a 3)(4 a 6a 9) 6. t 3 5 t (t 5)( t 5t 5) 8. 8 y 8 8 y 8 5 ( 4 y 4 )( 4 y 4 ) 5 ( 4 y 4 )( y )( y ) 5 ( 4 y 4 )( y )( y)( y) Factor the trinomial completely ( 8)( 8) 0. k 0k 00 k 0k 00 5 (k 0)(k 0) ( 4 49) 5 ( 7)( 7) 3. z 3 8 z 8z z 3 8 z 8z 5 z( z 8z 8) 5 z(z 9)(z 9) ( ) 5 5( )( ) ( 0 5) 5 3( 5)( 5) Determine the root(s) of each quadratic equation. Check your answer(s) ( 0)( 0) 5 0 ( 0) ( 0) or or The roots are 0 and m 6m m 6m (m 8)(m 8) 5 0 ( 8) 6(8) m m The root is Chapter Skills Practice
25 Lesson.5 Skills Practice page 3 Name Date ( 4 4) 5 0 6( ) 4() ( )( ) 5 0 6(4) The root is ( 3)( 3) ( 3 ) ( or ( 9 4 ) ( or The roots are and. ) ) t t 5 0 t t 5 0 (t )(t ) 5 0 ( ) () 0 0 t t The root is. 0. w 48w w 48w ( w 4w 4) 5 0 ( ) 48() (w )(w ) 5 0 (4) w w The root is. Chapter Skills Practice 64
26 Lesson.5 Skills Practice page 4 Determine the zero(s) of each quadratic function. Check your answer(s).. f() 5 5 f() (5 ) (5 ) ( 5)( 5) or or 5 5 The zeros are 5 and 5.. f() 5 4 f() ( ) ( ) 0 5 ( ) ( ) The zero is. 3. f() 5 9 f() ( 3 ) ( 0 5 (3 )(3 ) 9 ( 9 ) ( 3 ) ) or or The zeros are and Chapter Skills Practice
27 Lesson.5 Skills Practice page 5 Name Date 4. f() f() (3 ) 48(3) ( 6 9) 8(9) ( 3)( 3) The zero is f() f() ( 5 ) ( (4 5) 8 ( 5 4 ) ( 5 ) ) ( 5)( 5) or or The zeros are and f() f() (3 ) 5(3) ( 6 69) (69) ( 3)( 3) The zero is 3. Chapter Skills Practice 643
28 644 Chapter Skills Practice
29 Lesson.6 Skills Practice Name Date Could It Be Groovy to Be a Square? Approimating and Rewriting Radicals Vocabulary Choose the word that best completes each statement. square root positive (principal) square root radicand negative square root etract the square root radical epression. When solving certain quadratic equations, it is necessary to etract the square root from both sides of the equation.. Every positive number has both a(n) positive (or principal) square root and a(n) negative square root. 3. The radicand is the epression enclosed within a radical symbol. 4. A number b is a(n) square root of a if b 5 a. 5. An epression involving a radical symbol is called a(n) radical epression. Problem Set Rewrite each radical by etracting all perfect squares ? 5 6? ? 3 5 4? ? 5 5 9? Chapter Skills Practice 645
30 Lesson.6 Skills Practice page ? ? ? ? ( 63 ) Determine the approimate value of each radical epression to the nearest tenth < < < < < < 0. Solve each quadratic equation. Approimate the roots to the nearest tenth < 66.3 < 66.3 The roots are approimately 6.3 and m 5 68 m 5 68 m m < 68. m < 68. The roots are approimately 8. and Chapter Skills Practice
31 Lesson.6 Skills Practice page 3 Name Date 7. t 5 5 t 5 5 t t < 63.9 t < 63.9 The roots are approimately 3.9 and < 69. < 69. The roots are approimately 9. and ( 5) 5 ( 5) 5 ( 5) < 64.7 < < 0.3 or < 9.7 The roots are approimately 0.3 and ( 8) 5 9 Solve each quadratic equation. Rewrite the roots in radical form ? ? The roots are 4 3 and 4 3. ( 8) 5 9 ( 8) < 65.4 < <.6 or < 3.4 The roots are approimately.6 and ? ? The roots are 3 and 3. Chapter Skills Practice 647
32 Lesson.6 Skills Practice page ? ? The roots are 3 3 and ? ? The roots are 5 7 and ( ) 5 8 ( ) 5 8 ( ) ? 5 6 4? 5 6 The roots are and. 6. ( 0) 5 80 ( 0) 5 80 ( 0) ? ? The roots are and Chapter Skills Practice
33 Lesson.7 Skills Practice Name Date Another Method Completing the Square Vocabulary Define the term in your own words.. completing the square Completing the square is a process for writing a quadratic epression in verte form which then allows you to solve for the zeros. Problem Set Use a geometric figure to complete the square for each epression. Factor the resulting trinomial ( ) ( ) ( 6) ( 9 ) Chapter Skills Practice 649
34 Lesson.7 Skills Practice page ( ) ( 4 ) 4 Determine the unknown value that would make each trinomial a perfect square Determine the roots of each quadratic equation by completing the square. Round your answer to the nearest hundredth. Check your answer ( ) 5 0 ( ) <.6 or < 5.6 The roots are approimately.6 and 5.6. (.6) 4(.6) < 0 (5.6) 4(5.6) < Chapter Skills Practice
35 Lesson.7 Skills Practice page 3 Name Date (3.4) (3.4) (.4) (.4) ( ) 5 5 ( ) < < 0 < 3.4 or <.4 The roots are approimately 3.4 and (0.0) 0(0.0) 0 0 (9.80) 0(9.80) ( 5) 5 3 ( 5) < < 0 < 0.0 or < 9.80 The roots are approimately 0.0 and ( 6) 5 ( 6) < 9.3 or <.68 (9.3) (9.3) < 0 (.68) (.68) < 0 The roots are approimately 9.3 and.68. Chapter Skills Practice 65
36 Lesson.7 Skills Practice page ( 3 ) ( 3 ) < 0.30 or < 3.30 The roots are approimately 0.30 and (0.30) 3(0.30) < 0 (3.30) 3(3.30) < ( ) ( ) <.70 or < 3.70 The roots are approimately.70 and (.70) (.70) < 0 (3.70) (3.70) < 0 65 Chapter Skills Practice
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