Mini-Lecture.1 Eponents and Scientific Notation Learning Objectives: 1. Use the product rule for eponents.. Evaluate epressions raised to the zero power.. Use the quotient rule for eponents.. Evaluate epressions raised to the negative nth power.. Convert between scientific notation and standard notation. 6. Key vocabulary: eponential epressions, scientific notation. Eamples: 1. Use the product rule to simplify each epression. 9 7 a) b) m m m c) ( 6 y)(6 y) d) ( ab)( ab). Evaluate or simplify each epression. 0 0 0 a) b) c) ( 10) d) 0 ( + 1). Use the quotient rule to simplify each epression. 8 11 10y a) b) c) 7 y 6 1 y 9y d) 1 6abc 9 abc. Simplify and write using positive eponents only. a) b) ( ) c) y y 6 d) a e) f) 1ab g) a b 8 1 0 yz yz h) (a b)( a b ). Write each number in scientific notation or in standard notation. a) 6,000 b) 0.0061 c).6 10 d) 9. 10 Teaching Notes: Students need a lot of repetition and practice in order to master these objectives. Students often move constants along with a variable that has a negative eponent. For eample, in d) a common answer is a - = 1/(a ). Refer students to the eponent rule charts and the Writing a Number in Scientific Notation chart in the tet. Answers: 1a) 18, b) m 17, c) -6y, d) 1a 6 b, a) 1, b) -1, c) 1, d) 1; a), b) -y y, c), d) -9ab c ; a) 1 b) 1 9, c) 1 9 y d) a ; e), f) a 6 b 10 ; g) 9 1 z, a) 6.10, b).6110 -, c) 0.0006, d) 90,000 16, M- Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Mini-Lecture. More Work with Eponents and Scientific Notation Learning Objectives: 1. Use the power rules for eponents.. Use all eponent rules and definitions to simplify eponential epressions.. Compute, using scientific notation.. Key vocabulary: eponential epression, scientific notation. Eamples: 1. Simplify using the product rules for eponents. Write each answer using positive eponents only. a) ( ) b) ( y ) c) y d) ( m ) e) ( yz ) f) y g) 0 ( y z ) h) ( y ). Simplify using eponent rules and definitions. Write each answer using positive eponents only. a) a b c 9 b) ( ) c) 6 n m d) 10 7 y y 0 e) ( y) f) ( by) g) 1 z 7y y z h) 8 ( y ) ( y ). Perform each indicated operation using the properties of eponents. Write each answer in scientific notation. 8 9 a) (.9 10 )(6 10 7 ) b) ( 10 6 ) 1. 10 c) 10 Teaching Notes: Some students are confused by when to add eponents versus when to multiply eponents. Encourage students to write the eponent rules on an inde card to view while doing homework. Refer students to the Summary of Rules for Eponents chart in the tet. Answers: 1a) 6, b) y 6, c) d) y 9 1, e) 6 8y 6 y, d) 1 1 1, f) 6 by, g) y 7z 1 m, e) y z 6, f) 0 y 10, g) 6 1 9 y, h) 096y1 ; a) ab 18 c, h) 7 y ; a).910-1, b) 1.010-7, c).010 11 6 8, b) -6 6, c) 1 0 m n, M- Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Mini-Lecture. Polynomials and Polynomial Functions Learning Objectives: 1. Identify term, constant, polynomial, monomial, binomial, trinomial, and the degree of a term and of a polynomial.. Define polynomial functions.. Review combining like terms.. Add polynomials.. Subtract polynomials. 6. Recognize the graph of a polynomial function from the degree of the polynomial. 7. Key vocabulary: term, constant, polynomial, monomial, binomial, trinomial, degree. Eamples: 1. Find the degree of each polynomial, state how many terms it has, and indicate whether it s a monomial, binomial, or trinomial. a) b) 9 c) + d) y +. Define a polynomial function.. Simplify each polynomial by combining like terms. a) + b) 10y 8y c) y + y d) + 6 e) 9y + 8y + y f). Add the polynomials. + + + ( ) ( 6 7 ) a) ( y y ) (y 7) b). Subtract the polynomials. 6 + 9 a) 7 + 10 1 - - - - -1-1 - - - - y ( ) 6. Match each equation with its graph. 1 y + + 8y + c) b) c) ( ) ( ) 1-7 -6 - - - - -1-1 1 6 7 - - - - y M-6-7 -6 - - - - y 1-1 -1 - - - - 1 6 7 + ( 7 ) + 1) ) ) a) y = 1 Teaching Notes: b) y = c) y = + Most students find these polynomial operations easy. Tell students that identifying the degree of a polynomial is important for later work with factoring and solving equations. Remind students that this section is a review of distributing and collecting like terms. Some students forget to distribute the minus sign when lining up vertically. Answers: 1a) 1,1 monomial, b),1,monomial, c),,binomial, d),,trinomial; a), b) y, c) y+, d) -9, e) y+y, f) 6y + ; a) -y +1, b) - -10, c) 1 --, a) -6-10-1, b) +7, c) ; 6a)graph ; b) graph 1; c) graph Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Mini-Lecture. Multiplying Polynomials Learning Objectives: 1. Multiply two polynomials.. Multiply binomials.. Square binomials.. Multiply the sum and difference of two terms.. Multiply three or more polynomials. 6. Evaluate polynomial functions. 7. Key vocabulary: FOIL. Eamples: 1. Multiply. a) ( )( ) 10 b) ( 6a )( a ) c) (.1 y z ) ( 6 y z ) d) ( ) y( y + ) bz ( za + baz b) g) ( + )( + ) e) f). Multiply. a) ( ) ( ) + b) ( + )( + ) c) ( y ) ( 6y ) d) ( + 6)( + 6) e). Multiply. f) a) ( + ) b) ( c) ) ( + 7) y y 1 1 y y 6. Multiply. a) ( + )( ) b) ( y b) ( y + b) c) 1 + 6 b. Multiply. ( + ) 1 b) ( y ) c) ( y)( + y)( + y) a) ( ) ( ) 1 d) ( ) 6. If f ( ) =, find the following. a) f ( a ) b) f ( c ) c) f ( a+ b) d) f( a ) Teaching Notes: Encourage students to multiply binomials with FOIL mentally whenever possible. This will make factoring easier for them in future sections. Many students distribute the eponent when squaring a binomial, even after repeated reminders to multiply the binomial by itself. Refer students to the Square of a Binomial and Product of the Sum and Difference of Two Terms charts in the tet. Answers: 1a) 8, b) -0a, c).6 y 7 z 11, d) 6-8, e) -1y -6y, f) -ab z -ab z +b z, g) + ++1; a) +-1, b) ++6; c) 8y -1y+6, d) +1+6; e) - y +y 1, f) 1y y+ ; a) ++; b) -8+16; c) +1+9; a) -; b) y -9b 1 ; c), d) 6-b+b ; a) + -1+6, b) y -8y +y -y+16;c) - y-y -y ; 6a) a -a, b) c -c, c) a +ab+b -a-b, d) a -6a+8 Copyright 009 Pearson Education, Inc., M-7 publishing as Pearson Prentice Hall
Mini-Lecture. The Greatest Common Factor and Factoring by Grouping Learning Objectives: 1. Identify the GCF.. Factor out the GCF of a polynomial s term.. Factor polynomials by grouping.. Key vocabulary: greatest common factor (GCF). Eamples: 1. Find the greatest common factor of each list of monomials. a), b) 1, 0 c). Factor out the greatest common factor. 1, 0 d) 9 y,7y a) 16 1 b) 8 + 8 c) z z d) 18 + 9 6 e) 18ab 1ab+ 9ab 1ab f) ( y ) + ( y ). Factor each polynomial by grouping. a) y + y + + b) y 1 y + 6 c) y + 9 7y 6 d) y 10 + 7y 1 Mied Practice. Factor each polynomial. a) 16 1 b) 7y 18 + y c) 8abc 1abc 8ac+ 6a d) 9 y( z + ) ( z + ) e) y 8 + 7 y 1 f) + + + Teaching Notes: Remind students to check their factoring answers by multiplication. Some students need to rewrite the coefficients in problem in factored form in order to see the greatest common factor. Some students omit the 1 in the answer to Problem b). Many students are confused at first by factor by grouping problems where a negative sign must be factored out of the second grouping, as in problem b). Answers: 1a), b), c), d) 9y; a) (-), b) 8(+1), c) z(1-z ), d) (6+- ), e) ab(6a -+b-a), f) (y-)(+1); a) (+1)(y+), b) (y-6)(-), c) (y+9)(-7), d) (y-)(+7); Mied Practice. a) ( -), b) 9y(-y + ), c) a(ab c-6b c-c+), d) (9y-)(z+), e) (y-)(y+7), f) (+)( +1) Copyright 009 Pearson Education, M-8 Inc., publishing as Pearson Prentice Hall
Mini-Lecture.6 Factoring Trinomials Learning Objectives: 1. Factor trinomial of the form + b + c.. Factor trinomial of the form a + b + c a. Method 1 - Trial and Check b. Method - Grouping. Factor by substitution.. Key vocabulary: prime, perfect square trinomial. Eamples: 1. Factor each trinomial. a) + + b) + 6+ 8 c) 6+ 8 d) + e) f) 10 g) + 8 h) 18 i) + 1+ 16 j) y 6y + 8y k) +. Factor each trinomial. a) Trial and check method. a) y + 1y+9 b) 8 18+ 9 c) d) 7 1 0 e) 6 + 7 1 f) 6 + 6 6 y 7y 0y Factor the trinomials. b) Grouping method. g) 10 7 h) 0 + + 6 i) 8 11. Use substitution to factor each trinomial completely. 6 a) 6 b) 9 + 6 8 c) ( a+ ) + 7( a+ ) + 1 Teaching Notes: Some students can factor trinomials very quickly using the trial and check method. Some students become very frustrated with the trial and check method and appreciate seeing the grouping method because it provides a recipe that works for any non-prime polynomial. Remind students to always try to factor a GCF first. Refer to the end of section eercises for mied practice. Refer students to the Factoring a Trinomial of the Form the Form a + b + c by Grouping charts in the tet. M-9 a + b + c and Factoring a Trinomial of Answers: 1a) (+)(+1), b) (+)(+), c) (-)(-), d) (+)(-1), e) (-)(+1), f) (-)(+), g) (+6)(-), h) (-)(+), i) prime, j) y (-)(-), k) (-)(-1); a) (y+)(y+), b) (-)(-), c) (-)(+), d) (7+)(-), e) (-1)(+), f) y (-)(+); g) (-11)(+); h) (+)(+); i) (-11)(+1) a) ( -6)( +1), b) ( +)( -), c) (a+8)(a+7) Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Mini-Lecture.7 Factoring by Special Products Learning Objectives: 1. Factor a perfect square trinomial.. Factor the difference of two squares.. Factor the sum or difference of two cubes. Eamples: 1. Factor completely or state the polynomial is prime. a) + + b) 1+ 6 c) 9 + 6 + 1 d) 1+ 1 e). Factor completely. a) 9 b) y 10y y f) y 81 c) + 9y + 0y 1 z 16 ( ) d) + 6 e) 7 f) + 10+. Factor completely. a) + 8 b) +1 c) y 7 d) 6 e) p + 8q f) y + 1y g) ab 7b h) y + 0 Mied practice. a) 6 b) + 16 + 6 c) 1000y 1 d) 6y + 9y e) 18 98 + 6 f) ( ) Teaching Notes: Encourage students to always check if the first and last terms of a trinomial are perfect squares. If they are, then perfect square trinomial factoring may apply. Some students understand the difference of a square formula better if a) and b) are also done using trinomial factoring with a 0 middle term. Some students find the sum and difference of cubes formulas confusing at first and need to see many eamples. Remind students to factor out a GCF whenever possible. Answers: 1a) (+), b) (-6), c) (+1), d) (-), e) y (-1), f) prime; a) (+7)(-7), b) (y+9)(y-9), 1 1 c) + z z, d) (+11)(-), e) (+)(-), f) (++ )(+- ); a) (+)( -+), b) (+1)( -+1), c) (y-)(y +y+9), d) (-)(16++ ), e) (p+q)(p -pq+q ), f) y (+)( -+), g) b (a-)(a +a+9), h) (y+)(9y -1y+); Mied Practice: a) (8+)(8-), b) (+8), c) (10y-1)(100y +10y+1), d) (-y), e) (+7)(-7), f) (+11)(-) Copyright 009 Pearson Education, M-0 Inc., publishing as Pearson Prentice Hall
Mini-Lecture.8 Solving Equations by Factoring and Problem Solving Learning Objectives: 1. Solve polynomial equations by factoring.. Solve problems that can be modeled by polynomial equations.. Find the -intercept of a polynomial function.. Key vocabulary: polynomial equation, quadratic equation, standard form, zero-factor property. Eamples: 1. Solve each equation. a) 11+ 0 = 0 b) 6 + 1+ 6= 0 c) + = 70 ( ) d) + = e) ( 8) = + f) 1 + = 6 8 7 g) (+ ) ( 9) ( 1) = 0 h) = i) + 7 = 18 j) = 6 k) = +. Solve. a) One number eceeds another number by 6 and the product of the two numbers is 7. Find the numbers. b) A certain rectangle s length is feet longer than its width. If the area of the rectangle is 70 square feet, find its dimensions. c) One leg of a right triangle is 1 inches longer than the smaller leg, and the hypotenuse is 16 inches longer than the smaller leg. Find the lengths of the sides of the triangle.. Match each polynomial function with its graph. y y 1) ) ) 1 - - - - -1-1 1 - - - - -6-7 - - 1 - - - - -1-1 1 - - - - -6-7 1 g),,9, h) {-,0,}, i) {-9,0,}, j) {-8,0,8}, k) {-,-1,1}; a) 6 and 1, or, -1 and -6, b) 10 ft by 7 ft, c) 10 in, in, 6 in; a) graph ; b) graph ; c) graph 1 Copyright 009 Pearson Education, Inc., M-1 publishing as Pearson Prentice Hall - a) f ( ) = ( )( + ) b) f ( ) = ( 1)( + ) c) h ( ) = ( + )( ) Teaching Notes: Remind students to always put the equation in standard form before factoring. Some students try to use the zero-factor property before the equation is in standard form. For eample in c) : + = 70 ( + ) = 70 = 70, + = 70 etc. Many students find the applied problems difficult and need to see more eamples. Remind students to check whether their answers are reasonable for applied problems. Refer students to the Solving a Polynomial Equation by Factoring chart in the tet. Answers: 1a) {0}, b) {}, c) {0,-7}, d), ; a) {6,}, b),, c) {-10,7}, d),, e) {0}, f) {1,7}; -1 1-1 - - - - 1 y
Additional Eercises.1 Form I Name Date Simplify each epression. Write answers with positive eponents. 1.. 0 1.... t t 9 y y... a a. 6. 6. Write each number in scientific notation. 7. 8. 0.007 9.,00 7. 8. 9. Write each number in standard notation, without eponents. 10. 9.9 10 11. 7.6 10 1. 8.78 10 10. 11. 1. Simplify. Assume that variables in the eponent represent nonzero integers and that, y, and z are not 0. 1. y a y a 1. b c 1. z z 7 n 1. 1. 1. E-10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.1 Form II Name Date Simplify each epression. Write answers with positive eponents. 1. 7. ( + ) 0 + 0 1.... a b 1 7 8 ab 7 6... a 6a a. 6. 8 6. Write each number in scientific notation. 7. 0.006 8. 0.000001 9. 786,900,000 7. 8. 9. Write each number in standard notation, without eponents. 10..00 10 11..1 10 6 1..1 10 10. 11. 1. Simplify. Assume that variables in the eponent represent nonzero integers and that, y, and z are not 0. 1. y y a+ 1. a a 1. 1. 1. z z z t t1 t 1. E-10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.1 Form III Name Date Simplify each epression. Write answers with positive eponents. 1. 1. ( y )(6 y z ) 1.... 8 9 y z y z y y 9... a a a. 6. zy 8z y 6. Write each number in scientific notation. 7.,896,600,000 8. 0.00000 9. 7,800,000,000,000 7. 8. 9. Write each number in standard notation, without eponents. 10..116 10 11..06 10 1. 6.9786 10 6 Simplify. Assume that variables in the eponent represent nonzero integers and that, y, and z are not 0. 1. a+ 6 a 10. 11. 1. 1. 1. 1. y y nm k nm k z y z y b a c b a c 1. 1. E-10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form I Name Date Simplify. Write each answer using positive eponents only. 1. ( ). ( ) 1..... y. ( y ).. 6. z z z 6. Perform each indicated operation. Write each answer in scientific notation. 7. ( 10 6 ) 7. 8. 9..10 10 0.07 0.1 8 8. 9. Simplify. Assume that variables in the eponent represent nonzero integers and that all other variables are not 0. 10. (y n ) b 11. 1. b y a a y 10. 11. 1. Solve. Write the answer in scientific notation. 1. A certain computer can do a simple computation in 10 7 seconds. Epress how long it would take this computer to do this task 000 times. 1. E-106 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form II Name Date Simplify. Write each answer using positive eponents only. 1. ( ). ( 6 ). ( y z ). a b 6. ( y z 1 ) 1..... 6. a 1 a b ab 6. Perform each indicated operation. Write each answer in scientific notation. 7. ( 10 )(.1 10 ) 8. (.9 10 )(1. 10 ) 1 7. 8. 9..610 910 10 9. Simplify. Assume that variables in the eponent represent nonzero integers and that all other variables are not 0. 10. 11. 1. b ( ) a a a b b y7 y a a y y 10. 11. 1. Solve. Write the answer in scientific notation. 1. To convert from square inches to square meters, multiply by 6. 10. The area of a square is 9 10 square inches. Convert this area to square meters. 1. E-107 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form III Name Date Simplify. Write each answer using positive eponents only. 1.. ( z y 8 ) 1..... 9 7y 7 6 y z y y 6 10 1 6 y y... 6. (a 7 y 6 ) (10a y )(a y ) 6. Perform each indicated operation. Write each answer in scientific notation. 7. 0.00006 1000 0.00 0.00000 7. 8. (6. 10 )(1.6 10 )(. 10 ) 9. 7.110 10 710 10 8. 9. Simplify. Assume that variables in the eponent represent nonzero integers and that all other variables are not 0. 10. ( a 1 ) ( a+ ) 1 ( a ) 10. 11. 1. y y a1 a a a y y a a a a 11. 1. Solve. Write the answer in scientific notation. 1. 1. Find a cube s volume if each side is 0.07 meters long. E-108 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form I Find the degree of each polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. 1. 6.. 9 +. + 7 Name Date 1.... Perform the indicated operations.. (y + ) + (y + 1) 6. (7 + ) ( + ). 6. 7. 9y y6 y 1 7. 8. (8y 7) + (y 6) + ( y ) 9. ( + ) + (7 6 ) 10. (1y y + 6) (1y 8y 1) If P() = and Q() =, find each function value. 11. P(0) 1. Q( ) 1. P( 1) 1. Q() 1. A ball dropped from a cliff that is 1 feet above the ground. Neglecting air resistance, the height of the ball in feet at any time t, in seconds, can be described by the polynomial function P(t) = 16t + 1. Find the height of the ball at t = seconds. 8. 9. 10. 11. 1. 1. 1. 1. E-109 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form II Name Date Find the degree of each polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. 1. 6. 7 y. 7 +. y Perform the indicated operations.. (6y 11) + (6y ) 6. ( 9) + ( + ) 1..... 6. 7. 69 7. 8. 10y + 7 + y + 1 y 9. (11y y + ) (9y 7y ) 10. Find the sum of 10yz + y and 10yz + y 7. If P() = + 7 and Q() = 8, find each function value. 11. P( ) 1. Q() 1. P() 1. Q( ) 1. A projectile is fired upward from the ground with an velocity of 0 feet per second. Neglecting air resistance, the height of the projectile in feet at any time t, in seconds, can be described by the polynomial function P(t) = 16t + 0t. Find the height at t = seconds. 8. 9. 10. 11. 1. 1. 1. 1. E-110 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form III Name Date Find the degree of each polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. 1. 9. y y. y + 7 y. 6 + 7 1.... Perform the indicated operations.. (7 y 8y + ) + ( y + y ) 6. (19ab 1a b + b ) (0ab 8a b b) 7. ( y y + 7) ( y + y 8) 8. Subtract from the sum of 8 + and 6 10.. 6. 7. 8. 9. 10. 1 1 1 1 1 8 9. 10. 1 1 y y y y y y 7 9 9 9 9 If P() = + 7 6 and Q() = 9 +, find each function value. 11. P() 1. Q() 1. P( ) 1. Q() 11. 1. 1. 1. 1. 1. An object is thrown upward with an initial velocity of feet per second from the rim of a canyon. The rim is 80 feet above the canyon floor. Neglecting air resistance, the height of the projectile in feet at any time t, in seconds, can be described by the polynomial function P(t) = 16t + t + 80. Find the height at t = 8 seconds. E-111 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form I Name Date Multiply. 1. (7y)( 6y). ( )( ). (6 7) 1... Use the FOIL order to multiply.. ( + )( ). (y )(y 6) 6. ( 7)( + ).. 6. Use special product methods to multiply. 7. ( + 7)( 7) 8. (y ) 9. [ + ( + )][ ( + )] 7. 8. 9. Multiply. 10. ( )( + )( + 16) 11. (z + )(z )(z ) 10. 11. If f() = 1, find the following. 1. f(a + 1) 1. f(a + h) f(a) Multiply. Assume that variables represent positive integers. 1. ( n + )( n ) 1. ( n y m )( n + y m ) 1. 1. 1. 1. E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form II Multiply. 1. (1a b)( ab ). ( ab)(a ya ). (a + )(a a + 6) Name Date 1... Use the FOIL order to multiply.. ( )( + 8). (y )(y 7) 6. ( z)( + z).. 6. Use special product methods to multiply. 7. ( + y)( y) 8. (z ) 9. [6 (b )][6 + (b )] 7. 8. 9. Multiply. 10. ( 7)( + 7)( + 9) 11. ( ) 10. 11. If f() =, find the following. 1. f(y ) 1. f(a + h) f(a) 1. 1. Multiply. Assume that variables represent positive integers. 1. ( a y b )(y b a y) 1. ( n + y)( n y ) 1. 1. E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form III Name Date Multiply. 1. ( y)( 6 + y y ). ( )( + 1). (y 7)(y + y +1) Use the FOIL order to multiply. 1.... 1 1 6 9.. (y z)(y + 7z). 6. 1 1 8 y y 6. Use special product methods to multiply. 1 1 7. y y 8. [( ) + 1] 9. [ + ( + )][ ( + )] Multiply. 10. ( )( 1)( + ) 7. 8. 9. 10. 11. 11. ( )( + 10)( + ) If f() = +, find the following. 1. f(z + ) 1. f(a + h) f(a) Multiply. Assume that variables represent positive integers. 1. (y a b y)(y a b y) 1. ( y n+1 )(y n y n 1 ) 1. 1. 1. 1. E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form I Name Date Find the GCF of each list of monomials. 1.,,. y, 1 y, 8y 1.. Factor out the GCF.. 0 0. 8( ) + ( ). y(y + ) (y + ) 6. 1 18 + 7. 7y + 1y + 1y... 6. 7. Factor each polynomial by grouping. 8. + 10 9. y + y 10. ab 7a b + 1 11. 6 + 6 1. + 8. 9. 10. 11. 1. Solve. 1. The material needed to manufacture a bo with two square ends is given by the polynomial + y, where is the length of the square ends and y is the length of the other sides. Factor this polynomial. 1. An object dropped from 6 above the ground has a height of 16t + 6 feet after t seconds. Factor this polynomial. 1. 1. E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form II Name Date Find the GCF of each list of monomials. 1. 6 y, 18 y, y. 7 y, 8 y, 1 y Factor out the GCF.. 6a b 9ab. (y + 1) (y + 1). y y + 10 y 6 6. 7a 1 + a 1a 7. y + 1y 1..... 6. 7. Factor each polynomial by grouping. 8. 8y 6y + 9. 1 1 6 + 10. + y y 11. 1 + y y 1. + 6 8. 9. 10. 11. 1. Solve. 1. The material needed to manufacture a bo whose opposite sides are identical is given by the polynomial y + yz + z, where, y, and z are the lengths of the different sides. Factor this polynomial in terms of the reciprocals of each length. 1. An object shot from the ground with an initial velocity of 80 feet per second has a height of 16t + 80t feet after t seconds. Factor this polynomial. 1. 1. E-116 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises. Form III Name Date Find the GCF of each list of monomials. 1. y z, 18 yz, 9y z. 8ab c, 1a b c, 16a b c 1.. Factor out the GCF.. ab (b + 7) (b + 7). 16a b a b + ab ab. 1 y 8 y + 7 y 7y 6. y z 6y z + y z... 6. 7. m n m n m n 6 9 6 7. Factor each polynomial by grouping. 8. 6 z 1 + 10z 9. 1 8 y + y 10. mn mn n 6 11. a y b + a y 6b 6a y b a y b 1. Solve. 1 1 1 1 a b a b a b a b 6 6 m n m n m n m n 1. A design for a spherical metal shell is needed. The shell has a thickness of t, so that its inner radius is r and its outer radius is R = r + t. The volume of the material used for the shell is given by the polynomial R r. Factor this polynomial. Then rewrite the polynomial in simplest form in terms of the inner radius r and thickness t. 1. A model rocket is fired from the floor of a canyon that is 6 feet the canyon edge. If the object has an initial upward velocity of 18 feet per second, it will have a height of 16t + 18t 6 feet with respect to the edge after t seconds. Factor this polynomial. 8. 9. 10. 11. 1. 1. 1. E-117 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.6 Form I Name Date Factor each trinomial. 1. + +. 6. 1. 1 +. 7 + 6. 6 + 7 + 6 1..... 6. Use substitution to factor each polynomial completely. 7. + 8. 6 + + 9. (11 + ) + 9(11 + ) + 8 10. (y ) 1(y ) + 6 11. 6 + 17 18 1. + + 1 7. 8. 9. 10. 11. 1. Solve. 1. Find all positive and negative integers b such that + b + can be factored. 1. Find all positive and negative integers b such that + b + can be factored. 1. The volume V() of a bo in terms of its height is given by the function V() = 6. Factor this epression for V(). 1. 1. 1. E-118 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.6 Form II Name Date Factor each trinomial. 1. + 11 + 0.. + y 1y. y 16y + y. 1 + 17 + 6 6. 0y + 9y 0 Use substitution to factor each polynomial completely. Solve. 7. + 1 8. 6 9. (a + 7) (a + 7) 0 10. 19 11. ( + 8) + 11( + 8) 6 1. 6 17 + 1. Find all positive and negative integers b such that + b 1 factors. 1. Find all positive and negative integers b such that + b + factors. 1. The volume V() of a bo in terms of its height is given by the function V() = 1. Factor this epression for V(). 1..... 6. 7. 8. 9. 10. 11. 1. 1. 1. 1. E-119 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.6 Form III Name Date Factor each trinomial. 1. + 11y + 8y. + y + 8y. 8 16 10. + 11 1. 10 + 7 6. y 8 y 0 1..... 6. Use substitution to factor each polynomial completely. 7. + 16 + 1 8. 6 9. (a + ) (a + ) 10 10. 6 7 7. 8. 9. 10. 11. 1 17 1 (a ) (a ) 18 9 11. 1. 6 + 1 1. Solve. 1. Find all positive and negative integers b such that + b factors. 1. Find all positive and negative integers b such that + b 8 factors. 1. The volume V() of a bo in terms of its height is given by the function V() = 1. Factor this epression for V(). 1. 1. 1. E-10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.7 Form I Name Date Factor the following. 1. + + 1. + 0 +100. y 81. 0 +. ( 1) 16 6. + y 7. + 18 8. t 1 9. + 1000 10. b 8a 11. + 8 + 16 y 1. ( + 1) 1. ab 1000a 1. 1 + 9 y 1. 6 1..... 6. 7. 8. 9. 10. 11. 1. 1. 1. 1. E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.7 Form II Name Date Factor the following. 1. 6 80 +. y 11. 7 0y + y. y 6. 81y 100 6. ( ) y 7. + 1 + 6 y 8. a b + 1b 9. y 10. 1 + 8y 11. ( + ) 1. a 18a + 81 b 1..... 6. 7. 8. 9. 10. 11. 1. 1. 1 1 1. 1. 0y + y 1. m m + 6 n 1. 1. E-1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.7 Form III Name Date Factor the following. 1. 16 y + 8 y +. 9 + 9. 1 y y. 9y 900. 196 6. 6 + y 9 7. ( 1) + 8 8. + 9. 6 7y 10. 169b a + 6b a + b 11. a 16 1. 1 y 9 1. 7y + 1 1 1. 6 1. 6 y + y 1..... 6. 7. 8. 9. 10. 11. 1. 1. 1. 1. E-1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.8 Form I Name Date Solve each equation. 1. ( )( 6) = 0. ( + )( ) = 0. 8 = 0. + = 6. y = 1y 6. + = 7 7. 1 = 0 8. y = 6y 9. z 8z + 16 = 9 10. t t = t(7 + t) 11. = 1. ( + )( 7)( 9) = 0 1..... 6. 7. 8. 9. 10. 11. 1. Solve. 1. One number eceeds another number by 6 and their product is 91. Find the numbers. 1. A rectangular floor has an area of square meters. The length of the floor is meters less than twice the width. What is the length and width of the floor? 1. A board is leaning against a wall. The top of the board is feet above the ground, and the bottom of the board is feet from the bottom of the wall. How long is the board? 1. 1. 1. E-1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.8 Form II Name Date Solve each equation. 1. ( 1)( + 9) = 0. ( 1)( + )( 6) = 0. 10 + = 0. Solve. 1 0 10. 16 0 + = 0 6. 1 + 1 = 0 7. 8t = 6t 8. (9 10) = 0 9. ( 1) = + 10. t (7t + ) = t 11. + = + 8 1. ( + ) = 7( ) 1. If the sum of two numbers is and their product is 8 9, find the numbers. 1. A gardener wants to put a uniform border of gravel around the outside of a 16-foot by 0-foot garden. Find how wide the border should be if she has enough gravel to cover square feet. 1. A 10-foot ladder is placed against a wall so the bottom of the ladder is 6 feet from the bottom of the wall. How high from the ground is the top of the ladder? 1..... 6. 7. 8. 9. 10. 11. 1. 1. 1. 1. E-1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Additional Eercises.8 Form III Name Date Solve each equation. 1. (7 + 8)( ) = 0. 6( + 11)( 9) = 0. ( + 8)( 6)( 11) = 0. y y 16 = 0 1..... 1 10 0. 6. 1 0 0 7. (6 1)( + ) = 0 8. 9(t + ) t = 6(t ) 9. 7y + 1y = 0 10. 9 0 11. z + 7z = z + 1 1. Solve. y y 0 1. The sum of the square of two consecutive even integers is 80. Find the integers. 1. A contractor is going to lay a concrete sidewalk around a park. The park dimensions within the sidewalk are 10 feet by 110 feet. How wide will the sidewalk be if the contractor has enough concrete to cover 196 square feet? 1. A support cable runs from the top of a radio transmission tower to the ground. The distance between the base of the tower and the place where the cable is anchored is 90 feet. If the cable is 10 feet long, how tall is the tower? 6. 7. 8. 9. 10. 11. 1. 1. 1. 1. E-16 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Section.1 Eponents and Scientific Notation Objective: Calculate using scientific notation. Suggested Format: Small group format Time: 10 minutes Answer each of the following questions. You may wish to use a calculator. 1. Each side of a cube is.1 10 cm. Calculate the volume of the cube in cubic centimeters. Give your answer in scientific notation. 1. The distance light travels in one year is approimately.87 10 miles. How far does light travel in weeks? Write your answer in scientific notation, rounded to three decimal places.. According to the Medical College of Wisconsin, the average American consumes 8 grams of fat in a single day. If the population of the U.S. is 01,19,97 people, what is the total number of fat grams consumed by Americans in a single day? Write your answer in scientific notation, rounded to three decimal places. A- 1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Section. More Work with Eponents and Scientific Notation Objective: Write epressions containing positive and negative eponents in simplified form. Suggested Format: Think and Pair Time: 1 minutes Work each problem as quickly as you can. Speed is the goal in this part. Simplify the following. 1. 1.. ( 6) ( ) +.. y y.. Evaluate 0. ( 7 ) 0 y when = and y =.. +. Now work the following problems at a steady speed you are comfortable with. Then confirm your results on both parts with your partner. 1 6. ( 6 y ) 6. 7. ( ) ( ) + 7. 8. y 8. 0 0 0 9. ( y) ( ) + 9. 10. Evaluate y when = 1 and y =. 10. A- 1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form A Simplify each epression. Write with positive eponents. 1. ( )( )( 6) 1.. y y. ( ) ( 1 ab 8a b ). 1 a b.. Write in scientific notation: 6,000.. Write without eponents:. 10. 6. Use scientific notation to find the quotient. 6. ( 0.06)( 0.00008) 0.006 Perform the indicated operations. 7. ( 8) ( ) + + 7. 8. ( y + ) + ( y + ) 8. 9. y( + ) 9. 10. ( )( + ) 10. 11. ( ) 11. 1. ( 1)( ) 1. 1. ( )( + ) 1. T- 99 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form A cont d Factor each polynomial completely. 1. 6 y y 1 1. 1. + 10 1 1. 16. 9 + + 16 16. 17. 7 y 1 17. 18. + 18 8 18. 19. + 8 19. 0. 6 + y y 0. Solve each equation. 1. 6 ( )( + 7) = 0 1.. ( + )( 1) = ( ).. 7 + 1 = 0.. The sum of twice a number and its square is.. Find the number.. One number eceeds another number by 9,. and their product is 11. Find the numbers. T- 100 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form B Simplify each epression. Write answers with positive eponents. ( ) ( ) 0 1 6a b ab 1. a b 1.. a a m 1 m m a. a. ( y )( 9 y ) 1.. Use scientific notation to find the quotient.. 8 (.8 10 )( 1. 10 ).8 10. Write in scientific notation. 0.000007. 6. Write without the eponents.. 10 6. Perform the indicated operations. 7. ( y) + ( y) ( y ) 7. 8. Subtract 6 from 7 6 8. 9. ( a b)( a + b) 9. 10. 6y ( y)( + y) 10. 11. ( y) + 11. 1. ( )( + ) 1. Factor each polynomial completely. 1. 1. 7 7 1a b + 6a b 1. + 6 7 1. T- 101 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form B cont d 1. m + n 0mn 9 1. 16. 18 7 9 16. 17. 6 7 0 17. 18. a ab + a 8b 18. 19. 7 y + 8 19. Solve each equation. 0. ( )( + )( ) = 0 0. 1. + 9 = 0 1.. 9 = 6.. = 1.. A ball is dropped from the top of a 76 foot. building. Its height h ( t) at time t seconds is given by h ( t) = 16t + 76. Determine how long it takes the ball to hit the ground.. One number eceeds another number by, and. their product is 66. Find the numbers. T- 10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form C Simplify each epression. Write answers with positive eponents. ( ) ( ) 0 6 y 8 y 1. 1 y 1.. y. m+ 7. m m.. Use scientific notation to find the quotient.. 6 ( 1.8 10 )( 10 ) 9 10. Write in scientific notation. 0.0006. 6. Write without eponents. 7 8. 10 6. Perform the indicated operations. 7. ( + 11) ( + 1) + ( 8) 7. 8. ( 7y)( + y) 8. 9. y ( y ) 9. 1 10. + 10. 11. ( 7) 11. 1. ( 7)( + 7) 1. Factor each polynomial completely. 1. 18 y z y 1. 1. + 6 7 1. T- 10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form C cont d 1. + y + 0y 16 1. 16. 16 16. 17. m 81 17. 18. + 16y 18. 19. 1 + 1 6 19. Solve each equations. 0. ( )( 1) = 0 0. 1. + 7 6 = 0 1.. 8 = 0.. 6 ( ) = + 7.. The length of a rectangle is meters less than. twice the width. Find the dimensions of the rectangle if its area is 8 square meters.. One number eceeds another number by 7.. Their product is 10. Find the numbers. T- 10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form D Circle the correct answer. Simplify each epression. Write answers with positive eponents. 1. ( y) ( y ) 7y a. 1 76y b. 1 9y 9y c. d. 1 1 6 y 6. a a. 9a b. a c. 9a d. 1 9a. y z 6 y a. z 9 z b. 6 9 y 6 z c. 9 y z d. 6 y 0. 7 + ( 1 ) 0 a. 7 b. 8 c. 0 d.. Use scientific notation to find the quotient. ( 0.000 )(,000 ) 0.000 a. 9.6 10 b. 9.6 10 c. 9.6 1 10 d. 9.6 10 6. Write in scientific notation..6 10 6 a. 0.000006 b.,60,000 c. 0.000006 d. 6,000,000 Perform the indicated operations. 7. ( y + y ) + ( y y + ) a. y y b. 0 c. y + y d. y y y T- 10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form D cont d 8. Subtract ( ) from ( 6 + 6) a. + 7 + 1 b. 7 + 1 c. + 11 d. 7 + 1 9. ( + )( 9) a. + 1 + 108 b. + 1 + 108 c. 1 108 d. 1 108 10. ( + y)( 6y) a. c. 1y y b. 1y y d. 1y y + y y 11. ( y) a. 9 + y 1y b. 9 y 1y c. 9 y d. 9 + y 1. ( 7)( + 7) a. 16 8 9 b. 16 + 8 9 c. 16 + 9 d. 16 9 1. ( )( + 6 ) a. + 8 + 8 8 b. + 16 c. + 16 + 8 d. + + 8 8 Factor each polynomial completely. 1. 16 a b + 0a b a. a b( b a) b. a b( b + a) c. ab ( 8a b + 10a ) d. a b( 8b + 10a) 1. 6 + 6 1 a. ( )( ) b. ( 6 )( +1) c. ( )( ) d. ( + )( ) T- 106 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form D cont d 16. m + 9m 1m a. ( m + )( m 1) b. m ( m + )( m 1) c. m ( m )( m + 1) d. m ( m ) 17. 0y + y a. ( + y) b. ( y) c. ( y) d. ( y)( + y) 18. 6a + ab + b a. ( a + b)( b a) b. ( a b)( a + b) c. ( a + b)( a b) d. ( a b)( a b) 19. 16 81y a. ( 9y) b. ( 9y)( 9y) c. ( + 9y) d. ( + 9y)( 9y) Solve each equation. 0. ( + )( ) = 0 a., 0, b., 0, c., d., 1. 7 = 0 a. 1 1, b., c. 1 1, d., T- 107 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form D cont d. + 1 = 1 a. 0,, b., c.,0, d.,. A stone is dropped from a foot cliff. Its height h ( t) at time t seconds is given by h ( t) = 16t +. Determine how long it takes the stone to hit the ground. a.. sec b.. sec c. sec d. 6 sec. The sum of a number and its square is 0. Find the number a., 10 b. 10, c. 6, d., 6. A rectangular room with an area of 80 square feet has a width that is 6 feet more than the length. Find the dimensions of the room. a. 1 feet by 0 feet b. 0 feet by 6 feet c. 1 feet by 18 feet d. 16 feet by feet T- 108 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form E Circle the correct answer. Simplify each epression. Write answers with positive eponents. 1. a b( a b ) 1a a. b 6 a b. 8 6b a c. d. 9 b a b 8 7 y 9 y. y a. b. y y 18 0 c. y y 1 d. 17 a+ 1. a a. a b. a+ c. a+ d. a. ( a b ) 1 a a. 6 6b b. 1 1 6a b c. a d. 6b 6 a 6b ( )( ) 7.8 10. 10. Use scientific notation to find the quotient. a. 10 b. 10 c. 10 d..8 10 0. 10 6. Use scientific notation to find the quotient ( 10 )( 0.00 ).8 10 6 6 a. 19 10 b. 1.91 10 9 c. 10 d. 1.91 10 Perform the indicated operations. 7. ( 7 ) + ( + ) ( 9 ) a. b. + c. 16 + d. T- 109 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall + + 7
Name: Instructor: Date: Section: Chapter Test Form E cont d 8. ( y)( y z) a. 1 y z b. 1 y z c. 1 y z d. 8 y z 9. ( y)( + 6y) a. c. + y + 0y b. + 1y 0y d. y + 0y + y 0y 10. mn ( m )( m + ) a. c. m n 10mn b. m n + 6m n 0mn m n + 1m n 0mn d. m n + 6m 10n 11. ( 7 ) a. 9 6 + 16 b. 9 16 c. 9 + 16 d. 9 6 16 1. ( 8)( + 8) a. 9 + 6 b. 6 c. 9 6 d. 9 6 1. ( + )( + ) a. + + 1 b. 8 1 + 1 c. + 1 d. 8 + + 1 Factor each polynomial completely. 1. + 1 + 6 a. ( + 9)( + ) b. ( + )( + ) c. ( + )( + 1) d. ( + 6)( + ) T- 110 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form E cont d 1. 16 y y a. y ( ) b. ( y y) c. y ( 8 7) d. y ( )( + 6 + 9) 16. 8m + 1m 1 a. ( m )( m + ) b. ( m + )( m ) c. ( m )( m + ) d. ( m )( m + ) 17. 9m mn + 9n a. ( n m 7 ) b. ( m 7n)( m + 7n) c. ( 9m 9n) d. ( m + 7n) 18. + 0y + y a. ( + y) b. ( + y) c. ( + y) d. ( + y)( + y) 19. + 16 16 a. does not factor b. ( + 1) 16( + 1) c. ( 16)( + 1) d. ( + 1)( + )( ) Solve each equation. 0. ( )( ) = 0 a.,0, b. 0,, c.,, d.,, T- 111 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form E cont d 1. + 10 = 0 a., b., c., d.,. 1 = 18 a. 1, 6 b. 1,, 6 c. 6, 11 d. 1, 0, 6. ( + )( ) = + 6 a., b., c., d., A stone is thrown upward from the top of the cliff, which is 86 feet high, with an initial velocity of 8 feet per second. Neglecting air resistance, the height h ( t) of the stone t h t = 16t + 8t +. seconds after it is thrown is given by ( ) 86. When will the stone hit the ground? a. 10 sec b. 9 sec c. 6 sec d. sec. Find the height of the stone when t =. a. 896 feet b. 800 feet c. 70 feet d. 16 feet T- 11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form F Circle the correct answer. Simplify each epression. Write down with positive eponents. ( ) ( ) m n m n 1. 8m n a. 0 b. 8 18m n c. 1 m n d. m 1 n y. 1 y 1+ y a. 1 y b. y 1 c. y 9 d. 6 y ( )( ) 6.7 10 10. Use scientific notation to find the quotient. 9 10 6 a. 0.9 18 10 b. 9 0 10 c. 0.9 10 d. 9 10. 1 0 6 + + 0 a. 8 b. 6 c. 11 d. 7 Perform the indicated operations.. Subtract ( ) from ( 6 8) + a. 10 + b. + 11 c. 10 + d. + 7 6. + a. b. c. + d. + 1 T- 11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form F cont d 7. m n ( m )( n 1) a. m n + 6m n b. c. 0 d. 9m n + 6m n m n m n 6m n + 6m n 8. ( 6 ) a. 6 16 b. 6 + 16 c. 6 8 16 d. 6 8 + 16 9. ( 8)( + 8) a. 9 6 b. 9 + 6 c. 9 + 6 d. 9 + 6 10. ( a + b)( a b) a. 1a b c. 1a + 7ab 10b d. 7ab 10 b. 11. ( )( 7 + ) 1a + ab 10b 1a ab + 10b a. 9 b. 19 + c. + 9 + d. + 19 + Factor each polynomial completely. 1. 10 y y a. y ( + y) b. y ( y) c. ( y + ) d. y ( + y) 1. 18 8y + 98y a. ( 7y)( + 7y) b. ( + 7y ) c. 6( 7y) d. ( 7y) T- 11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form F cont d 1. + 6y y 1. a. ( 8 7y)( + 7 y) b. ( 16 y)( + 7y) c. ( 8 y)( + 7y) d. ( 8 + y)( 7y) 1a 8b a. ( a b)( a + 0ab + b ) b. ( a b)( a + 10ab + b ) c. ( a b)( a + 10ab + b ) d. b ( a b)( a 10ab + b ) 16. 10b + 19b 18b a. b ( b 6)( 8b + 1) b. ( b + 6)( 8b 1) c. b ( b 6)( 8b 1) d. ( b + 6)( 8b 1) 17. + + 9y a. ( 7y)( + 7y) b. ( + 7y)( + + 7y) c. ( + 7y)( + 7y) d. ( + 7 y) 18. 6a b a. ( 16a b ) b. ( 16a + b )( a b)( a + b) c. ( a b) ( a + b) d. ( 16a + b )( 16a b ) Solve each equation. 19. 7 ( + 7)( ) = 0 a. 7,0, b. 7, c.,0, d. 7,0, 7 0. 0 = 0 a., 10 b., c., d. 10, 1. 11 + = a. 9 9, b., 9 c., d. 9, T- 11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall
Name: Instructor: Date: Section: Chapter Test Form F cont d. ( 8) = a., 1 b. 8, 1 c., 1 d., 8. 8 ( ) = 6 9 a., b., c., d.,. If the cost, C ( ), for manufacturing units of a certain product is given by ( ) = 0 + C, find the number of units manufactured at a cost of $60. a. 6 units b. 8 units c. 70 units d. 9 units. The product of two consecutive even integers is less than times the smaller one. What are the numbers? a., 6 b. 0, c., d. 6, 8 T- 116 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall