University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

139

Pages:

4
Author:

Wildmotivbu7o

Factoring Polynomials a Essential Question How can you factor a polynomial? EXPLORATION: Factoring Polynomials Work with a partner. Match each polynomial equation with the graph of its related polynomial function. Use the x-intercepts of the graph to write each polynomial in factored form. Explain your reasoning. 1. x2 + 5x + 4 v@ = 0 - 2x3 6. -4 -4 4 -6 /0. 6 -4 -4 - -6 6 -4 -4 x2 + 2x = 0 Notetaking with Vocabulary In your own words, write the meaning of each vocabulary term. factored completely I+ ? 0 I y f'\ 0 Mt� I C�Mf\e!.+tjr f/\0 j � ��vi quadratic form 4, (.., ti,f " d ft•-......e ��- ftMtlC �lly ,h, Core Concepts -i, Sum of Two Cubes j;_d- (a+ b)(a' - ab+ b') f � Difference of Two Cubes �a3 - b3 \ = (a - b)(a2 +ab+ b2 ) . ,......... ...... r1'-\ ; (.I. / 64x {"b,) 3 l - 1\.-..b--l.- &,., \,•f!.. l( 27x - 8 -J« m • � � 4- ;- "t: --z.. - '-'l i - 1-- o -£1(2-- t-5 f! A. � ; Ii f' f,t;, �;1- cH � /;\, +13 = {4x + l){l6x2 -4x + l ,, • • ("-.'f-) �}' (1) = . 3 - 23 . = (3x - 2)(9x2 + 6x + factor by grouping � 1,y,f.-t trt ti. 0 c-t t;111b�'K f,.,f{�11 ( t., Y-'1 p / \ C �� -1 Example Example ----••' ..... -•· j _I M" IC(. p O Jy Special Factoring Patterns �$-( ' 4) Also L, MM.01\ 11 CoMo'f\ v�-,,-thL�.5 D � P+·e-ft"//I ( l O f s'1 � '-( Tr\AO'Mi';l s S1 11L't"'�� N ;(\)Ii\ .,. S+ y I e., ) H.L;) Extra Practice In Exercises 1-14, factor the polynomial completely. 1. 20x3 (Ort\M,(h'\ 220x 2 + 600x - � ) f-�M W x. ( Y-. 'I. + �o') 11 ;x - \ �·:�� 10 rµ, x(x-5)(;><.-"� @ 1.- f·!;;-.,�m.+.,')(rt1 +-ct ) lll)vv cD111-1pletc. 3. 27a 3 + 8b 3 S"'m ofi C"'bes (I); (i.b) ( " � b '\( a 2- -=-( 4. = 3 -� b + 6-i..) l:-- 5t4 5t 6 + 2t 5 (rt :, � ( L: ·_ -ti - - t. > (r 2t3) f 2.. t ;')( 5 c +-2') '- o+l-b1(( ) -(; )(tb t(tbY) � I c�" + n1 <"" 2. - "'"' b f ,..l % 1 ' ;,•/(; '-t , l l... (; c 1. +3 '){ y1--t ; ) G� -lb) c .��c:: O -l7, 1 -\ -l * 16. -12 + \ -t 1'2- �12.- (01 f(x) = 6x3 2- & Jo + 8x2 'if /'2.. Cf 2,0 f (?( ;. � - - 34x - 12· x - 2 -",'-I -l'Z... �1 o � I 70 :,, l ( (o ,,/- i-- 2-0 -; ': .• ! : +b (oMM.0� L. (@;>'1,,. 4 I Ox +. 3 1 ( 'i- � + tDx + q� ( X t -/'\('I--+ 4 f(x) - � \ � - l'2.. • \0 Cf ( 12x + 6x2 + 20x x - 5 • +- t. + -lO - t.D .. ()( -5) ( z_,/' - 2-)( Lot'l"I M-OV\ l-0 -2-0 '2- - O A '-i )(� 2.-)( ( )( 1.-_ � -2..) � r:·,. l )C. (x -s ,(x·H ')()(-1. I\ 3 -� J (3 X 1( Y- + 3)\ il ,;,_\'A�Y� ir1 ff or\ + t(.,_) ,,f!. ( 11. :i J_)