6. 6 v ; degree = 7; leading coefficient = 6; 7. The expression has 3 terms; t p no; subtracting x from 3x ( 3x x 2x)

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1 70. a =, r = 0%, = a = 000, r = 0.%, = a =, r = 00%, = 7. ( ) = 0,000 0., where = ears 7. ( ) = + 0.0, where = weeks 7 ( ) =,000,000 0., where = das 7 = 77. = 9 7 = 7 geomeric 0. geomeric arihmeic, 6, 96, 9, 9 9 9,, 6,, 7, 0,, 6, 6,,,, a =, an = an Chaper 7 7. Sar Thinking Sample answer: Objec Leer How Man Epression able couch c c ligh balloon b 6 6b movie m 0 0m An epression showing he sum of all he erms above is 6b + c + + 0m Warm Up Cumulaive Review Warm Up. ( 7, ). (, ). ( 6, ). (, ) 7. Pracice A h + h ; degree ; coefficien = ; rinomial = leading p + 0; degree = ; leading coefficien = ; binomial 7 6 v ; degree = 7; leading coefficien = 6; monomial 7. The epression has erms; + v 0. j j + 0. w w + +. p +. w. + + b b 7 The negaive sign should no disribue o 7 in he linear erm in he second line. ( + ) + ( ) = ( ) ( 7) ( 6) = = + 7. p pq q no; subracing from ( ) = does no ield he same resul as subracing from = ( ) 7. Pracice B ; degree = ; leading coefficien = 0, rinomial + π degree = ; leading 9 coefficien = ; rinomial n n n; p ; degree = ; leading coefficien = ; monomial 7. rinomial; degree = q q q k k + 7 Coprigh Big Ideas Learning, LLC Algebra A77

2 ... + w w 7w g 6g 6g 0 + w 7. m mn + 9n g gh h ; when =, h = f 7. Enrichmen and Eension f 7. 9f 9f 7. Cumulaive Review Warm Up. As increases b, increases b. The rae of change is consan. So, he funcion is linear.. As increases b, is muliplied b So, he funcion is eponenial. 7. Pracice A q q The is subraced in he second facor, so he firs column should be. ( )( ) Puzzle Time BY ITCH-HIKING 7. Sar Thinking Sample answer: 0. 0 = u + u + m + 7m. w + w Epression Answer ( )( ) The answers o he firs wo epressions are he same, as are he answers o he las wo epressions. The firs wo epressions are relaed because he second epression is an epanded form of he firs epression where he firs se of parenheses is broken ino wo erms and he Disribuive Proper is used on he second se of parenheses. The las wo epressions are relaed in he same manner. 7. Warm Up 7 ( ) ( ) 7 ( z )( z ) + 7 ( ) ( z ) zz b q q h h h no; The degree of he produc is he sum of he degree of he binomial and he degree of he rinomial. 7.. Pracice B.. p p + 0. v v p + p r r A7 Algebra Coprigh Big Ideas Learning, LLC

3 7. The erm was added as a erm insead. 0.. = z + z p p p r 9r r 0 m + m + g 7 d 7d + 0d + + Sample answer: + = 6 7. Enrichmen and Eension. 0 A = + + P = + 9, 7. Sar Thinking ( )( ) + = + 9 = 9; The resul is onl he wo erms because he middle wo erms cancel each oher ou; The firs erm in he answer is he square of he firs erm in each se of parenheses and he second erm is he square of he second erm in each se of parenheses. Sample answer: = = 9; Yes, he previous eplanaion will hold rue for an number; ; Because he middle erms will no cancel ou in he epressions ( + )( + ) and ( )( ), here will be hree erms in he answer: These epressions boh feaure duplicae facors, so he can be rewrien + and, respecivel. as ( ) ( ) 7. Warm Up.. +. z z a + 7ab + 6b 7. Cumulaive Review Warm Up. =. =.. 0. =.. =.. A = +, P = + 6 A = + P = +, 6 + = + 0. =. 7. Pracice A w w Puzzle Time BY PASSING THE BUCK 9. 6q + 6q v 9 6 a 9 p n 6 0. ( 0 )( 0 + ) = 00 = 99. ( 0 )( 0 + ) = 00 = 99. ( 0 + )( 0 + ) = = 09 Coprigh Big Ideas Learning, LLC Algebra A79

4 . Onl he firs and las erm of he square of a binomial paern are presen. = +. a. ( ) = + b. A = 6 f ; The original room has he larger area, 900 f Pracice B p 6 p g 6 9u 9s 9 9c 6cd + d 6q 9m 6n c 0. ( 0 + 7)( 0 + 7) = = 79 = = = = 6 6. The consan erm should be ()( ) = ( + )( ) =. a. = 0,000π 00π + π b. 0,000π π Puzzle Time VANISHING CREAM 90π 6π 7. Sar Thinking + + = 0would be rewrien as The equaion ( a)( b ) = 0; The equaion is equal o zero, so eiher a = 0orb = 0 mus be rue; This means ha eiher + is equal o zero or + is equal o zero; The wo resuling equaions are + = 0 and + = 0. The soluions are = and = ; The soluions are he numbers ha can be pu ino he original equaion o make he equaion rue. 7. Warm Up. =. = 6. =. = 7 = = 7. Cumulaive Review Warm Up. < 6. z. n. m > z 9w 7. k = 6 6 f Sample answer: a = 0, b = ; a =, b = Enrichmen and Eension... A0 π π π + + π π + π Algebra. 7π π + π 0 7. Pracice A 6. = 0 and =. d = 0 and d = Coprigh Big Ideas Learning, LLC

5 . = 0 and = 7. = and = p = and p = q = 7. = 0 = 0, =, and = u = 0, u = 9, and u = 0. = and =. = and =. + ( ). k ( k ). ( ) = 0 and = 7. n = 0and = 7 = 0 and n = The second erm of he polnomial was los when facoring in he second sep. + = 0 + = 0 ( ) = 0and + = 0 = 0and = = 0and = ; imes when frog jumped and landed. 7.. Pracice B. = 0and =. d = 6andd =. w = andw =. h = 0, h =, and h = = and = 0. = and = 6. = and =. v( v + ). r ( r ). 6 ( ) a a + h = 0andh = w = 0andw = 7. n = 0andn = The Zero-Produc Proper was used incorrecl b no firs rewriing he equaion o make he righ side equal o zero. = = 0 ( ) = 0 = 0 and = 0 = 0 and = = 0; es, Sample answer: ( ) ( ) = 0 7. Enrichmen and Eension Puzzle Time HORSE THAT WAS SO SLOW DURING A RACE THAT THE JOCKEY KEPT A DIARY OF THE TRIP k = 0andk = 7. = 7and = 9 n =, n =, and n = n =, n = 6, and n = Coprigh Big Ideas Learning, LLC Algebra A

6 7. Sar Thinking Sandard Form The sum of he consan erms from each se of parenheses is he coefficien of he -erm in he sandard form of he polnomial. Likewise, he produc of he consan erms from each se of parenheses is he consan erm in he sandard form of he polnomial. 7. Warm Up.,,, 6, 7,,,.,,, 6, 7,,, 0.,,, 7,,.,,, 7,,,, 6,,,,, 6, 0,,, 0, 0, 60,,,, 6, 9,,, 6 7. Cumulaive Review Warm Up. nonlinear; You canno rewrie he equaion = in = m + b form, due o he quadraic erm.. linear; You can rewrie he equaion = + in = m + b form, wih m = and b = 7. Pracice A Facored Form ( 6) ( + ) + ( ) ( ) ( ) ( ) + ( 6) ( ) + Sum of Consan Terms Produc of Consan Terms 7. ( + )( + ). ( + 6)( + ). ( z + )( z + 7). ( w )( w ) ( )( ) ( )( 7) 7. ( + )( ) ( + )( ) ( m + 9)( m ) 0. ( n + )( n ). ( d + )( d ). ( z + 7)( z ). a. b. 6 f. Alhough ( )( 6) =, he cross-erms sum o 6 = 9, no + = 9 lengh = f, widh = f base = cm, heigh = cm 7. as desired. = 0; If = is a soluion, hen ( + ) is a facor. If = ( ) is a facor. So, he equaion mus be ( + )( ). 7. Pracice B is a soluion, hen. ( + )( + ). ( w + 7)( w + ). ( + )( + ). ( )( 9) ( j )( j ) ( m 9)( m 0) 7. ( + 7)( ) ( w + )( w 0) ( b + )( b 6) 0. ( p + )( p 9). ( q 7)( q + ). ( + 9)( ). Alhough ( )( ) = 96, he cross-erms sum o + =, no as desired = +. base = 0 m, heigh = m lengh = cm, widh = cm a. The zeros of he polnomial correspond o is facors. b. ( )( + ) 7. Enrichmen and Eension. ( + )( ). ( b c)( a c). ( + 6)( + ) A Algebra Coprigh Big Ideas Learning, LLC

7 . ( )( + ) ( v + )( v ) ( )( ) 7. ( )( z + p) ( + )( + ) + = ( ) ( ) = ( ) ( ). Sample answer: ( 7)( + ) = + = ; ( ) ( ) Yes, he produc of wo binomials can alwas be facored again b grouping.. Eercise 9 has four erms, whereas Eercise 0 has hree erms afer simplificaion because wih onl one variable, like erms can be combined. 7. Puzzle Time A FROG ON A COLD DAY 7.6 Sar Thinking Sample answer: The lis of facors is used o find he coefficien of he -erm in he sandard form of each polnomial. To do his, mulipl pairs of facors, choosing one se from each lis, and hen add he producs o ge he coefficien of he -erm. 7.6 Warm Up. ( ). ( + ). ( z z ). 7 ( + ) ( ) ( + 6) ( + )( ) 0. ( p + )( p ). ( v + )( v 6). ( v )( v + ). Neiher facor has a negaive -erm, which is necessar o make he leading coefficien negaive. + = +. = and = 7 p = and p = =, 7. =, = sec =±, ±, ±, ±, ± 0. ( a + b)( a b). ( )( + ) 7.6 Pracice B. ( + )( ). ( 6)( + ). 6( + )( + 7). ( )( + 9) ( p )( p + ) ( w + )( w + ) 7. ( + 7)( ) ( 6j )( j ) ( d + )( d ) 0. ( 9v )( v + ). ( 7m + )( m ). ( 0q + )( q ). The produc of he binomials on he righ side has a consan erm of, insead of. ( ) 6 + = Cumulaive Review Warm Up. = + 7. = 6. w = and w = 6 = and = Pracice A. 6( )( + ). ( + )( ). 9( )( ). ( + )( ) ( + )( ) ( )( + ) 7. ( + 6)( ) ( 9)( + ) =, 7. widh =, lengh = 0 =, 7 =±, ±, ±, ±, ± 77, ± 0. ( r + s)( r + s). ( + )( ) Coprigh Big Ideas Learning, LLC Algebra A

8 7.6 Enrichmen and Eension. ( + )( + ). ( + )( + ). ( p + 7)( p ). ( )( + ) ( )( + ) ( v )( 0v ) 7. ( u + )( u + ) ( d + )( d ) ( + )( + ) 0. ( )( + ). Sample answer: 0 = Puzzle Time WITH A SAND DOLLAR 7.7 Sar Thinking 6 = ; The facored form ( + )( ) is equivalen o he original epression because when muliplied ou, he middle erms cancel, leaving 6; + = + + ; ( ) ( ) = + + = Warm Up Cumulaive Review Warm Up. (, ). (, ). (, ). (, 0 ) 7.7 Pracice A ( + 6)( 6). ( 7 + )( 7 ). ( + )( ). ( 7 )( 7 + ) = 6 ( 6 6)( 6 + 6) = + = 7 7. ( k + 7) ( m 9) ( + 7). v = ±. p =. q = 7. = ± ( + )( ) ( ) 7. 9( + ) sec p + p + 6 = p + 6 a. canno be facored; ( ) 0. a = b. canno be facored; ( ) b. in.; 9 =, = 7.7 Pracice B. ( 0 + 7)( 0 7). ( s + )( s ). ( + )( ). ( 6 )( 6 + ) = 0 ( 9)( + 9) = ( 7)( + 7) = 7. ( z + ) ( ) ( 9a + ) 0. a. +. b. no; 60 < 6 9 = ±. w = 0. s = 9. = 6 ( + )( ) 7( p + ) 7. ( ). sec a. canno be facored; q + q + = q + 6 b. canno be facored; = ( + 7) 0. a. + b. cm A Algebra Coprigh Big Ideas Learning, LLC

9 0. a. 6 b. 0 in.; 6 = 6, = Enrichmen and Eension a + 6a b + ab + b a a c + 90a c 70a c + 0ac c. ( + )( ). ( p + )( p )( p + ) ( )( ) + no facorable 7. + ( ) q( q + )( q ) ( + )( ) 0. 7( + + ) a 6a b + a b 0a b + a b 6ab + b j = 0,,. w = 0, ± 6. =, ±. = 0, 7, Puzzle Time IN THE DICTIONARY 7. Sar Thinking Polnomial GCF a es; I is common o encouner a polnomial conaining a GCF ha can be facored ou, leaving a rinomial ha ma be facored using one of he oher echniques lised in he able. 7. Warm Up Cumulaive Review Warm Up Pracice A + b + c a + b + c Difference of Squares ( + )( ). ( + 9)( ) = 0, ± 7 = 0,, 7. a. V = 6 9 b. cm 7cm cm ( a + b)( a + )( a ) ( g h)( g + )( g ) 7. Pracice B. ( a + b)( a ). ( m + )( m + 7n). ( )( + v). ( + )( ) ( + )( ) w ( w ) 7. ( p + )( p )( p ) 6 ( z z + 7) 7h ( h + )( h ) 0. ( + 7)( 7)( + ). p =, ±. = 0,,. = 0, ±. = 0, 7. a. V = 9 b. in. 9 in. in. q =, ± = 0,, ( )( + 7) ( p q)( p + q) 7. Enrichmen and Eension. ( + 6)( + ) Coprigh Big Ideas Learning, LLC Algebra A

10 . ( )( + )( )( + ) 0.. ( p )( p + ). ( )( + )( + ) + ( + )( + ) ( ) ( ) 7. ( u + )( u + ) ( d 7)( d ) ( + )( )( + ) 0. ( )( + )( + )( + ) 7. Puzzle Time VERY COOL ANSWERS Cumulaive Review. w =. = π. =. 9 < < no possible < or > a b = 7( ). = ( + ). + = ( + 7). ( 9, ) (, ) (, ) a w b. 0 weeks z and 6 rz z %.7% () ( ) f = , where is in ears. () ( ) f = , where is in ears () ( ) f = , where is in ears = 6 7. =,, 0. 6,, 6.., 0,,, 6,,,.,, 96, 7, 960, 67,. + 7 ; binomial 7 6w w 7 w; + rinomial A6 Algebra Coprigh Big Ideas Learning, LLC

11 π z + z + z ; rinomial 7. g + h v + v ( u )( u ) 90. ( z + )( z + ) ( )( ) ( r 7)( r 7) ( g )( g ) sec 9 ( + 0)( 0) 9 ( h + 6)( h 6) ( b + )( b ) 9 ( k + ). 7w w 0w 7 9 ( a ) 00. ( 0g + 9) 0 0., 7. n n + 0 r + r 0. 7, 7 repeaed roo a b. 7 f w 0. ( + 6)( + ) 0. ( )( 7 + ) 0 ( w + )( w ) m 6m h 0 ( )( + 7) 6 a b. square unis 67., 6, Chaper Sar Thinking Sample answer: , Quadraic equaion Shape Relaionship o = 7. 0, 7.,0 7. 0, 7. ( + )( + ) 7 ( + )( + ) 7 ( w + 9)( w + ) 77. ( )( ) 7 ( d )( d ) 7 ( z 0)( z ) 0. ( m + )( m ) ( z + 6)( z ) ( )( + ), 6, 9 ( + )( + 6) ( + )( + ) = U-Shape slighl narrowed = U-Shape slighl widened = ( ) upside-down U-Shape = U-Shape reflecion in he -ais moderael narrowed The value of he coefficien of he -erm deermines how wide or narrow he graph is, and if negaive, shows a reflecion in he -ais; Sample answer: The graph of = looks he mos differen because i is refleced in he -ais. 7. 6( w + 0)( w + ) ( + )( + ) Coprigh Big Ideas Learning, LLC Algebra A7