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120_10.4_notes

# 120_10.4_notes - Mat120 Chapter 10 Section 4 Analyzing FOIL...

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Unformatted text preview: ( Mat120 Chapter 10 - Section 4 Analyzing FOIL multiplication four (4) situations Fac’tzored Form: F O I L L- a. (1% x + L! x + 5 X + I L K;/ Factored Form: F O I L 3. (x—3)(x-4) X ,. qx~3x +!3\ Factored Form: F O I L (x—3)(x+4) XL+HX*‘75X “ll. Factored Form: F O I L (x+3)(x—4) x ,_ ‘W +3 X 49‘ Page 10 Trmomlal X 3% 7 x + I L . 15°?“ U/v/‘u‘r Jr 1% O Trmomlal X ‘3— 7 x (,L Mat120 Chapter 10 - Section 4 Page 11 Factoring Tﬁnomials Two Methods. --- First method is a factoring by grouping method. / Alternate Method: http://www.purplemath.com/modules/facguadhtm Given a polynomial of the form: ax2 + bx + c Step 1: Take a - c Step 2: List at the factors of a 0 c, want the sum or difference of those factors to be equal to b. Let those factors to be p and q. So p+q = b or p—q =b Step 3: Rewrite the using those polynomial as: (You have recreated the inner/outer product.) ax2+bx+c =ax2+px+qx+c Step 4: Factor by grouping. IC \$51" 50”” 4:" ° LL 1/ Example: x2+14x+24' a= / and c=1Ll Soa-c= 2L! X" /\ I+o=1ct 1241=+w=5‘.11/ +906 +1396 +9~¢f wand: lnwleom 2.1; 21-13-qu 03mm“! (X—nxh- (ox—law ) W me / ><Cx+4)+{;(‘x+,x) £3?“ng 364-3 avidly 420% V (“(+4) (x+l>_)_} r60H" ’ W tr 23+ 0 Example: x2 — L6x + 8 a X1//\ I+o== b 5’- q ll \ ﬂ? 5 an 6 ll tag (/2 O h? o (3 II ~2~X - 4x+87 (X—Ax)—-;L{>l+c?) / XCX?A)'~*‘¥"3) ((x—;)(><—-‘+)i WSW Example: 5x2 + 14x +8 14‘" a: 5‘ and c: 5)” So a.c= 1710 9. 331%) =H 40'! 40H: fxwox +4x+g 9.0,; goo—zoo; (“it“) +(L/X+?] 10 "I 10+¢I=Iq/ 5'x(x +9.) + Lf6x+4> V Macon (5M4) 7 Mat120 Chapter 10 — Section4 Page 12 Two Methods. --- Second method of factoring is a reverse foil method. “Cris-Cross Straight Across " Given a polynomial of the form: ax2 + bx + c Step 1: List the factors of both a and c and analyze the expression Step 2: Set up a table of the following type: F (for First! Llfor Last) List the List the factors of a factors of c so that their so that their product is a product is c Step 3: Check the Outer and Inner terms by cross multiplying the factors of the ﬁrst and the last terms. (That would be the inner/outer terms.) Step 4: Choose the one that gives you the right center term (b). Step 5: Get the correct factorization by writing across. Example: A 2 . x + 8x + 12 Analyze. + W ﬂm a = | I + 0 Factors: ,4 . 2. a. 2 3044‘ 7L 3 - 4 for First L! for Last) ’% \$0104- 1 ’2‘ 2.. x ><L Q ”E7 W CCU/a44— __., 1/4+’?_. ___? X+3~ Chapter 10 - Section 4 ' 0 ~‘( L( ) E_(far First} [Afar Last”; I 3 a3 WWH II nope. ¥ ff“ /‘° 7“ ( (a 9 WI. , ‘ ><A a; __, 1 ﬁg, X—‘ 5 ((x—aﬂxi-t-I) Thaw. ”-9 I ”7 Ll X+‘/ Bar—72+} Analyzg I+O:‘7 3= 1 6= 3 12a2£~ Factors: 1 1' 1-3 F__(fm' Filsﬂ 14111701 Last) Ejfm First)_ Lifer Last)_ 1 I .1 i 3 -(o 2‘>< 5 3 L><‘ a" fholat. “‘7 7 } .. 5 ,——7 x~b H 2 .. \-‘? ozx—z 3x3 — 10: —. 3 Analyze a— m 2 I? O “ “/0 Facbrs: X '1 3 “ 7 I .- 4 '2. F (for First) Lifer Last) F_(fo:r Fnst) Lffm' Last} 9 ><3 5 L, (3 L I I g ,2 X] j» inapxd at HOP—L 9/ 64. 6x2 — Sxy — 6yz Mat120 Chapter 10 — Section 4 Page 14 Factor Complewa --- For now it means remove the Greatest common factor ( if necessary) ’ ’ 1‘ _ 32. 4xz—4x—8 4(Xix~i) 510014 meet) 50. 5y1 + 33y — 14 (S‘g‘A)(‘j+7) / (9x92- 9x3 +\4 X3 ‘63; Lox“.QX‘e,LS+( 4X34. 3") 3x(ax«a 9)+29(ax-%9J (Axawxaqu) 70. 10x3+24x2+14x a-C: 527 :35-- P+g= 1L 4x(5Xﬁ/Ax+7) @ /7\$7.7.:[.L 3* (X+{)15X+73 2, +5“+7:{-/L 5X +12~><+ 7 5VW\$7+7x+77 (6‘)?“ 9X +( x 7 5x<><+n + 7CX+13 Lx44JC5X+7j ...
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120_10.4_notes - Mat120 Chapter 10 Section 4 Analyzing FOIL...

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