University:
Bradley University
Course:
MTH 109 | College Algebra
Academic year:

2019
Views:

176

Pages:

10
Author:

Cale Mejia

Adding Polynomials ( 3 b2 —8 b - 5) + ( - 2 b2 + 5 b + 9) Unit 3 3b 2 - % y -r - Addition & Subtraction of Polynomials 2b2 + Sb + i ALGEBRA 1 Adding Polynomials (6 X3 — 4 2 * + 4) + (8 * 2 &% ^ 4 4 Nx 3 3 f- 2 -7x 2 -3 7 + 2 x2 — 7) (5 a - 3b) + ( 2a + 6b) A . 3a - 9b B . 3 a + 3b (C ]) 7a + 3 b D. 7a - 3b ^ 1 >4~ * <\ Zb fish 744 Si? 9/16/2019 Subtracting Polynomials (5a - 3b) -> (2a + 6b) (6w4 +2>v2 - 2) + (7 w4 — 4vv2 + 3 w) . lA ^ (X - 3u) - 7^q + a 7 2 "3w i/ jq + 6> wo - ^ - - 1) + ( ~ 2 ?x 2- 3 x- i 2 i/ x - ^ • £ ( ) 3 a - 9b B. 3 a + 3b C. 7a + 3b D. 7a - 3b Subtracting Polynomials (9X2 3X Lr xz + 2 x - 4) ~ 23 ' (tb 3« -% 9/ 16 / 2019 FOIL Unit 3 . lF: FIRST 3.1: INSIDE T T~ ALGEBRA 1 / Y 'TLL ojd), . 4 L: LAST 3 5 2 + 5 A: ) 2 tLcY /S %r 3 A: (8A: FOIL 3 8 2 X ( 4A: K# 1 7 2A: ) ( A + B ) {C + D ) (5 A: - 3 )(10A: - 1) l T + B )( C + D ) ( A + B )( C + D ) CA + fl)(C + /> ) ITH <. DISTRIBUTIVE PROPERTY — ( A + B )( C + D ) 2.0 : OUTSIDE ( A MULTIPLYING POLYNOMIALS MiJTply Y/vi ( A + B )( C + D ) ( 2 x + 5)(3 A: + 9) J . lF: FIRST 50 * - S - 3p +3 * * L* 1 / (>4 + B )( C + D ) + £)(C + D ) (4 + £) (C + D ) (4 + £)(C + D ) 2.0: OUTSIDE ( A 3.1: INSIDE . 4 L: LAST 9/16/2019 |V BINOMIAL TIMES A TRINOMIAL FIND THE SQUARE —r (8m - 4)P (% 32 2 - ^ fa V rr + ( 2 x 2 - 3 )( 5 X 3 - 4 X + 8) (3m + 7) 2 2- ( 3 r*+ ^ | TZ—/ 2 ivi + H 2 / + W * , * 23;t3 +l7»7 + 2 - ? 4 ID ' BINOMIA\ L TIMES ATRINOMIAL BINOMIALTIMES A TRINOMIAL (2p + l)(p 2 — 3p + 4) (A:2 5^: 4- 4)(2 A: ( 2' X S )[ TC 7 - S:X y- v ) - ?/ 2 - Ibifrf' X < If - ' a' 4- 2 S'? / ’ T - /fy » ^ - 200 7 ' ^ 5) 0 _ '4 9 / 16 / 2019 Word Problem Word Problem A polynomial expression is shown below. ^ N A polynomial expression is shown befew? ex(4x3 + 8x2 - 12) - (x2 + 4)(x2 + 6) - (14X5 + 7X3 + x) (x + 29)(2nx2 + 1) The expression is simplified to 27X4 + 56X3 10x2 - The expression is simplified to 14X5 - 17X3 - 696X2 - 29 ( Wyf + ht What is the value of n? A. 12 B -8 C. 8 I Mx ' /7 What is the value of e? * / The expression is simplified to -15X3 + 20x?'+ 75x. What is the value of /? A. 15 B. 3 D. -15 (s ^' jrrz ^ X ' So) + 2 2S> x ' 5 y l *20x P°A °^ ' -3 0 2 / SrxS - Sfr / l/ j* / - - Mv - n S< ^ / 5“ -/2 - 7'- W ' t#' a w . • Is 59 Gi S*( > cr - 84x - 24 h' jW Z- 4 . ^ th S> - 5) - -/f ^ • -V?5 6) r 7T ‘ \i i ' ll m [ bJ X 6 bawW 9 / 16 / 2019 . ^yu \ cLatSnV - in i s® ftf:- 2 FACTORING OUTTHEGCF 27 x 8 y 4 -6 - 2. V; Unit 3 s - 3>x FACTORING POLYNOMIALS > ALGEBRA 1 TRR- 1 0r - f T . iff - 2 V36 -- 6 ff - i ffl l t ' f f :| j/A - % ' x3 + % x6 + 14 -2 i fiffoo -fO nf5T - n ifffZ -I z /y ' Tff&r - / $- Z -Z - 22 _ U 7,3 z ^- x * fiff/ - 12 Difference of Two Squares 20 A 2o 7 • 10 $ ¥ ~ @» r 32 / 32 - 2 lC x 6 -144 12 X* 1. Factor Out a GCF. (If Possible) Find the Squares of the First Term . 4. a2 Find the Squares of the Last Term Put the 1st Term in the 1st Place of Each (), Put the Last Term in the 2nd Place of Each () — b2 = ( a + b )( a - b ) A7- ^ /0 9/16/2019 6 f + /- • - ( -+ l s% % > 4 k 4 - 100h2 H - 5 2 « / KT J -& / 0£ ^ 1. Factor Out a GCF. ( If Possible ) 2. Find the Squares of the First d2 + lid 4. Put the 1st Term in the 1st Place of Each ( ),, Put the Last Term in the 2nd Pliace of Each () a2 + 28 1. 2 )\ ^ 4-T \ Find the Squares of the Last Term ( - )l )( -X - ) 4 ^ TRINOMIALS ( A = 1) Term 3. o) - \ ( + )[ - ) * [ - ) l + ) ' Difference of Two Squares 2 Sx2 - 64 /*y iw X 2 +H x lH 9 3. Check for GCF Write two sets of parenthesis, )( ). These will be the factors of the ( trinomial Think of factors of c that add up to b (Use Chart for Signs) ^ EB — b 2 = (a + b)(a — b ) + + + Both Both Factors are + are Factors — Bigger Bigger Factor Factor is is + - 70 9-K JO • I I - 3 It ' ll) TRINOMIALS ( A =l) d 2 + 3d JZ iH - 18 3 W -\ x 4 -2 / G s' u -S 6# tOW OY ' \l ( 3. TRINOMIALS ( A =l) Check for GCF Write two sets of parenthesis, )( ). These will be the factors of the trinomial. Think of factors of c that add up to b . ( Use Chart for Signs) k 2 + 6k f - 2 7 f 2 21 t li M B + Both Factors are + Bigger Bigger Factor Factor is + is - 2. JL Jl-I X + Both Factors are - . 1 3. Check for GCF Write two sets of parenthesis, ( ) ( ). These will be the factors of the trinomial. Think of factors of c that add up to b . ( Use Chart for Signs) B or ( - ?f ) 4 ± + Both Factors are + + Both Factors are - Bigger Bigger Factor Factor is + is - *) I 9/16/2019 Gff : OM TRINOMIALS (A =l) TRINOMIALS (A =l) x3 V -20 I 1. 2. 2 2/ 3. 7» 1 + 16 x 2 - 40 ^ H -S 5 X 2 *-| Or 0.4x 2 - 2.8 x + 4 ! i the trinomial. Think of factors of c that add up to b . ( Use Chart for Signs) B 2 [ Mb )[ y ~2 ) ^ * Check for GCF Write two sets of parenthesis, ( )( ) . These will be the factors of Both Factors are + m> Both Factors are — Bigger Bigger Factor Factor is is + i •lt> * ' 'S MS -9 x 3 - 18x 2 + 135 1. 2. 3. l is - ly Both Factors are + Factors are - Bigger Bigger Factor Factor is + is - + + Both Both Factors Factors are are + — Bigger Bigger Factor Factor is is + gTfo .TRINOMIALS (A = 1) for GCF 3 x 2 - 3.3 x + 5.4 1. Check of parenthesis, Write ' 2 I /V 0 7 ‘ °\ K + + Both B - Check for GCF Write two sets of parenthesis, )( ) . These will be the factors of ( the trinomial. Think of factors of c that add up to b . ( Use Chart for Signs) B Check for GCF Write two sets of parenthesis, )( ). These will be the factors of ( the trinomial . Think of factors of c that add up to b ( Use Chart for Signs) uio TRINOMIALS (A = 1) ' 3. 1 + + |; I 0 -1 two sets ( )( ). These will be the factors of the trinomial. 0,3> j 3. Think of factors of c that add up to b . ( Use Chart for Signs ) B WX + Both Factors are + + Both Factors are - Bigger Factor Factor is + is Bigger - 9 / 3 /lOVi .Simplifying Polynomials Simplifying Polynomials 9y 2 7y 5 + 8y 3 &/V B / %z Vf5 - KSC: v.,;. r /5 I I Cyn )lv -t) ( V’ r **h iT £t -i )C ' r y- x* i x -r ^ y- v) .nVj • . x 2 + 3 x — 28 x 2 - 9x + 20 Aw 24 y ( 7y 2 -?) * Simplifying Polynomials x2 x2 T + lx + 12 - 5x - 24 y 2 f 7m * Simplifying Polynomials I B I y T x2 + Sx — 33 (x + ii)(x + 3) . jo VfV - 3 $ / ( fYn? ) ^ C wihly - ti I _ X- J yh/ ' —— Xxrfh- y) MB ., IMMBKM y •> ' » *rm CaMtHr - i) -' - ... . .. .. - v,. I V -z yt ' -J ' i - 9/3/2019 Simplifying Polynomials lx 2 5(x + 1) - 28x - 35 Simplifying Polynomials Simplify the following expression B / 5x7 Gcf - i s(w ) L h' -2f r r / 7 7 T i l x* iy -s) * 3~ . #T 4 A 1 B. 5r 7 C. ~5r 9 °* £S> ( Simplifying Polynomials 2 — S T 28x 4- 48 4x 8 x 2 - 40 x + 48 *< y Z n(pC -1x >-o) q r * Vr -r) \ J16 B _^__* * *- ?*' / t* - * P -'r ) l xYz - w ) 5V Simplifying Polynomials GCAzfr 2xy ? % - % ntx^ SrH ) B. . 2x — C 2 xy2 0 -y " -~ ?y ^W - K S**!1] *, - ? 8r 2y f 3 x 2 y2 +4 I? 7 - T r ? ya * 8y f 4 _ — 8xV + 4 ?xv ( 2#/ \j - y x+ t e u Y -t h 2h-2) Citf- 2 Simplify the following expression. +4 % _ 45 - 9x12 5V?. V i-x 7 5 x *U s? " x3 7/ . s z 2 T * 2

Adding Polynomials

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