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Excellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a `" 0 and a, b, and c are real numbers. Click the here to return to the presentation.VmBTime To Check Your Understanding.o This is an incorrect response to Check Your Understanding.This is a binomial. Click here to return to the presentation.VpBTime To Check Your Understanding.drP This is an incorrect response to Check Your Understanding.This is a binomial and a =0 so it does not have the term ax2. Click the here to return to the presentation.tExcellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a `" 0 and a, b, and c are real numbers. Excellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a `" 0 and a, b, and c are real numbers. Click the here to return to the presentation. x~jFactoring Trinomials of the form ax2+bx+c with a =1.F/ 0|DTimes New Romanh bbd 0 b & 0DComic Sans MSnh bbd 0 b & 0B DSymbolans MSnh bbd 0 b & 00DArialans MSnh bbd 0 b & 0"@DArial Unicode MS bbd 0 b & 0" ` .  @n?" dd@  @@`` H(I2      ob$ ʍ hGB%:b$\Mnf'K:2$!՗'RAHq5eD2$?3iIuI3y2$ =)A2$.7ESnu|^Mc 1?33@8{ uʚ;mNʚ;g46d6dd 0bppp@ <4!d!dg? 0bib<4ddddg? 0bib<4BdBdg? 0bib? %O = lFactoring Trinomials of the form ax2+bx+c with a ! 0.n7$C$K$ C$cCC$ Dr. Marcia L. Tharp Why learn to factor trinomials? Factoring trinomials is an important Algebraic skill. It is used in higher-level mathematics and science. Besides that you will need it to simplify polynomial expressions and solve more complex equations.  Lesson 1 - Recognizing The Form ax2+bx+c with a ! 0^F4C$K$ C$c C$  The trinomials we will factor that have the form ax2+bx+c where a ! 0 and a, b, and c are real numbers. zp6#+##%#" More Examples Let s look at some more examples where we will replace the values a, b, and c in the form ax2+bx+c. u' \'/'"'" i What happens if we let a=0, b=3 and c =4 when we replace the values a, b, and c in the form ax2+bx+c ? j'$^'/'"'"^Lets try letting a=0, b=0, and c=5 when replace the values a, b, and c in the form ax2+bx+c. h_U'/'"'!Time To Check Your Understanding.""  Check your understanding. Click on the expressions below that fit the form we want to factor. Remember we want to use polynomials of the form ax2+bx+c where a ! 0 and a, b, and c are real numbers that are not binomials. a. x2+6x+8 b. x2+16 c. 2x+8 d. 2x2+7x+6  0ZIZ'/'c<'&" ckckckcCz  m 0 lm 0 m 0om 0  m 0$)rm 0)- m 016tm 06>m 0 m 0 m 0m 0 m 0$)m 0)-m 016m 06>NNow click on the door to go on to How to factor the form ax2+bx+c with a =1 O#BfFNF$$""m 0#:  Excellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a `" 0 and a, b, and c are real numbers. Excellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a `" 0 and a, b, and c are real numbers. Click the here to return to the presentation.NT%-2%$ T'/2'&" ,'&<VA jm 0*.m 0*.  This is an incorrect response to Check Your Understanding.This is a binomial. We cover factoring binomials in another lesson. Click here to return to the presentation.^M'" /" *'mm 0m 0  This is an incorrect response to Check Your Understanding.This is a binomial and a =0 so it does not have the term ax2. Click the here to return to the presentation.M'"('/'".'pm 0m 0  ` f [f f3̙` 999f~` ___` 33f3f` f33f 3f3̙` 33f̙3f>?" dd@(33?Zd@ 33 d " @ `"  n?" dd@   @@``@n?" dd@  @@``PN   @ ` ` p@@ %  z(  ^T   "  Tgֳgֳ?P < 2   Tgֳgֳ? < 2 Z  s *A?8    f1 ?"   T Click to edit Master title style! !Z    f1 ?"   RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S   # ld1 ?"  X*  # lPĸ1 ?"   Z*  # l ɸ1 ?"  Z*N  6޽h? ? f [f f3 Lock And Key1   % @  W(   |T    "    f}gֳgֳd? < 2     `gֳgֳ?`  < 2 Z   s *A?|   # l`1 ?" U   T Click to edit Master title style! !   f1 ?" t  W#Click to edit Master subtitle style$ $  # l\1 ?"0   X*  # l,1 ?"    Z*  # l1 ?"  Z*N  6޽h? ? f [f f3  0p$(  pr p S   U   r p S   p  H p 0޽h ? f [f f3̙  P$(  r  S      r  S     H  0޽h ? f [f f3  ~v`t(  tr t S       t S  p<$  0  r t ZԔ?0  ,$D  0 .For example in ax2+bx+c Let a=1, b=2 and c=4 j/ Z'33/33'33' 33< t  f1? 0,$D  0 rnThen we get a trinomial 1x2+2x+4 Remember 1 x2 means x2. So we can write x2+2x+4 too which fits this form. n Z 2'33/33'33/33'33/33'33/33 '33H t 0޽h ? f [f f3̙  =5px(  xr x S  @ 8   Z x  `81??0I,$D  0 This time we get a trinomial 3x2+20x+12 which fits the form we are going to try to factor. since a ! 0 and a, b, and c are real numbers. ^ 2"'/A'+'33` x c $A ??$ h  Q x ZXԔ?,,$D  0 WIf a=3, b=20 and c=12 do we get a trinomial that will fit our form that we will factor? X 2X'H x 0޽h ? f [f f3̙F  |(  | | ZԔ?@3,$D  0 What happens if we let a=4, b=0 and c=25? Will we get the trinomial form we need when we will replace the values a, b, and c in the form ax2+bx+c? L 2%-%u |  f,1?!P ,$D  0 CInstead we get the binomial 4x2+25 which we will not factor here. LD 2%-$% |  ft1?l P},$D  0 FIt only has 2 terms so it is not a trinomial we are going to factor. This fits the form since a ! 0 where a, b, and c are real numbers. However, we won t discuss this here since we have already covered factoring binomials. j 2`%''}% H | 0޽h ? f [f f3̙  1)(     <(Ԕ  p<$D 0   X   fs1?``,$D 0 This is not a trinomial of the form we need because a=0. The x2 term is missing so it does not fit the form. It is a binomial. So we will not discuss factoring it using the methods in this section.  2'''''/''   fls1?``N,$D 0 LAnother Example   2'$G   fs1?|`,$D 0 }We get 0x2+3x+4 = 3x+4.J 2 ' / ' H  0޽h ? f [f f3̙  /(     <t sԔ     s    fs1?0P ,$D 0 7This is not a trinomial because a=0 and b=0. It is a monomial. Furthermore the x2 term is missing since a equals 0 and it does not fit the form we are looking for above.r 2' ' 9' / X' V   fs1?,$D 0 We get 0x2+0x+5 = 5 \ 2 ' /  ' ' H  0޽h ? f [f f3̙h   (  r  S s    s   S $s   s "p`PpB   fD1? 0    `1?@xm 0m 0H  0޽h ? f [f f3333    J(  r  S j     r  S j      S Ac:\Program Files\Microsoft Office\Clipart\standard\stddir1\bd07236_.wmfLP @ m 0m 0H  0޽h ? f [f 333333B  (  r  S 8s    s   C Ac:\Program Files\Microsoft Office\Clipart\standard\stddir1\bd05214_.wmf  H  0޽h ? f [f f30  p(  r  S Bs `  s   C A~c:\Program Files\Microsoft Office\Clipart\corpbas\j0078711.wmf0 H  0޽h ? f [f f3j  (  r  S Fs `   s H  0޽h ? f [f f3 xUNAvP!ĂX 1Q4QJC#`‹Xjceb|,gsvo/ؠ|=vfg۹_/o 4 SC"p%LӴ#O>u`5zH"*6lC1 E?\ 7:L{6NQΜͿFWPs3E1GjU;Kh!-}Yռ30MrocʗV6:vVMfRiii}Cd[He|p/xE>`Օ*"ӃT*iI,rC s2B` Uy;nDN1)0q[VgPײ:Jgˤs%nڑ1h"u2*l)UWN3ܜyƼCe/bbIrP0,9 0BFqLURY,`#eDhkm'pts{,( Oh+'0LR px$ 0< \ h t ,Factoring Trinomials of the form ax2+bx+c.Dr. Marcia L. 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Why learn to factor trinomials?HLesson 1 - Recognizing The Form ax2+bx+c with a ‡ 0wMore Examples Let’s look at some more examples where we will replace the values a, b, and c in the form ax2+bx+c. PowerPoint Presentationj What happens if we let a=0, b=3 and c =4 when we replace the values a, b, and c in the form ax2+bx+c ? _Lets try letting a=0, b=0, and c=5 when replace the values a, b, and c in the form ax2+bx+c. "Time To Check Your Understanding.ONow click on the door to go on to How to factor the form ax2+bx+c with a =1 YExcellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a ≠ 0 and a, b, and c are real numbers.         Excellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a ≠ 0 and a, b, and c are real numbers.       Click the here to return to the presentation. This is an incorrect response to Check Your Understanding.This is a binomial. We cover factoring binomials in another lesson.    Click here to return to the presentation. This is an incorrect response to Check Your Understanding.This is a binomial and a =0 so it does not have the term ax2.   Click the here to return to the presentation.  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles p  8@ _PID_HLINKSA( 6(262,8,Time To Check Your Understanding.U265,10,Excellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a `" 0 and a, b, and c are real numbers. Excellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a `" 0 and a, b, and c are real numbers. Click the here to return to the presentation.(262,8,Time To Check Your Understanding.266,11, This is an incorrect response to Check Your Understanding.This is a binomial. Click here to return to the presentation.(262,8,Time To Check Your Understanding.267,12, This is an incorrect response to Check Your Understanding.This is a binomial and a =0 so it does not have the term ax2. Click the here to return to the presentation.U265,10,Excellent you recognized the trinomial did have the form we are going to factor: ax2+bx+c where a `" 0 and a, b, and c are real numbers.