EXPONENT. Section 2.1. Do you see a pattern? Do you see a pattern? Try a) ( ) b) ( ) c) ( ) d)
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1 Section. EXPONENT RULES Do ou see pttern? Do ou see pttern? Tr ) ( ) b) ( ) c) ( ) d) Eponent rules strt here:. Epnd the following s bove. ) b) 7 c) d) How n 's re ou ultipling in ech proble? ) b) c) d) Wht opertion is hppening between the eponents of the se bses?. Epnd the following s bove. ) b) c) Wht opertion is hppening between the eponents of the se bses?
2 Review: ) t t ) ) ) 9 ) t t ) ) ) v N z ) ) ) ) 7) t t t 7) ) ) 9) b c b c b c 9) 0) rt r t 0)
3 Section.,.,.: More RULES EXPONENT eponent bse. p p e/. p p e/. b b How n bses re their? b b ) z z E/ b) z z. p p e/ e/ e/ 0 Now for the fster ethod: c z z
4 . p p Wht does the negtive eponent do? E/ E/ 9 b b Wh did the inside flip? b b b b Siplif: b b b bc
5 z z q p q pq k k k
6 .: Polnoils, dding nd subtrcting Degree of Polnoil Identif the following polnoils: Descending order 7 Leding Ter Leding Coefficient The constnt (no vrible)
7 7 + + The nuber in front tells ou how n ou hve ² + ² ( )-( - + )
8 .: Polnoils, ultipling Review: 7 7 b b Monoil (polnoil) 7 Binoil Binoil The ctul ultipliction F O I L
9 Binoil Trinoil Y Y Y ) Find: i) perieter ii) re b) Find: Are Siplif: b b b b 9
10 .: Polnoils, dividing Dividing b Monoils - - Dividing b binoils, trinoils, etc q q 909 q q q q q Steps: ) ) ) ) q q q q q Answer: 0
11 0 7 q q q 9 7
12 Section 7.: Fctoring: GCF nd -ters. How to find the GCF GCF = 7 7 GCF =. Divide out the nubers the hve in coon. GCF= 00 0 GCF= Find the GCF. ) ) )
13 FACTORING Distributing Fctoring FACTORING OUT THE GCF EX / Fctor + + Wht is the gretest coon fctor? EX / Fctor + + Wht is the gretest coon fctor? Do the two ters hve n in coon, how n? EX / Fctor + c + c Wht is the gretest coon fctor? Do the two ters hve n in coon, how n? Do the two ters hve n other coon fctors?. Siplif. Fctor 9. Siplif. Fctor
14 . Siplif zz z z. Fctor z z z z 7. Fctor c c. Fctor 0 b c b 9. Fctor 0. Fctor 7 )Fctor ) Fctor 7 TERMS Bo Method Fctor b Grouping q q q q `
15 Section 7.: Fctoring: -ters: fctoring trinoils es X X X X The lst two nubers ultipl to give ou the third ter. The lst two nubers dd to give ou the iddle ter X X ) Wht two nubers when ultiplied give ou the lst nuber (find the fctors of ) Test nubers : ) Wht se two nubers when dded give ou the iddle nuber (dd the fctors of ) ) X X ) Check it X - b - c or + b - cthen one of the nubers is -, - b + c then both of the nubers re negtive. b c then both of the nubers re positive.
16 . Fill in the blnks. () To fctor + +, ou need two nubers tht dd up to nd hve product of. Then + + = ( )( ) (b) To fctor - +, ou need two nubers tht dd up to nd hve product of. Then - + = ( )( ) (c) To fctor - -, ou need two nubers tht dd up to nd hve product of. Then - - = ( )( ) d) To fctor + -, ou need two nubers tht dd up to nd hve product of. Then + - =. Fctor ech trinoil. In ech cse, check b ultipling our nswer. This llows ou to check to see if our nswer is correct. eple: b + b - 0 = (b - )(b + ) check: (b - )(b + ) = b + b - 0, so the nswer is correct. No check=no credit () (b) + - (c) 0 (d) (e) 7 (f) 0 g) h) i) j) 0
17 Section 7.: Fctoring: -ters: fctoring trinoils c Multipl the following: FACTORING TRINOMIALS prt 0 Soething new, so little different Wht two nubers when ultiplied give ou (-0)= Wht se two nubers when dded give ou the iddle nuber Setting the proble up ) Wht two nubers when ultiplied give ) Wht se two nubers when dded ou ou the nuber -0 give ou the iddle nuber - Test nubers nd + nd + nd + nd + nd + nd + ) So nd 0 So we chnge - into 0 Now we need to fctor it The Bo Method or Fctor b Grouping. Group (Don t forget bout the negtive). Fctor ech group 7
18 Hint: coon fctor Hint: descending order
19 Section 7.: Fctoring: -ters: b b b b b b
20 A Look for coon FACTORS. Fctor + Fctor - - b b b -TERMS b b b b b b b b 7 -TERMS Wht two nubers when ultiplied give ou the lst nuber (c) X X nd when dded gives ou the iddle nuber (b). Bo Method - TERMS Fctor b Grouping q q q q 0
21 Section 7.: Solving 0 Wht do ou think the nswers re? Solving using fctoring 9h 0h 0 0 7
22 Section 7.: Applictions of solving ) An envelope's length is c ore thn its width. The re is 9 c. Find the length nd the width. Define Length= Width= Eqution : Eqution : ) The bse of crdbord bo hs width tht is feet less thn the length. The re is 7 ft. Find the length nd the width. Define Length= Width= Eqution : Eqution : ) A rectngulr sig is twice s long s it is wide. If its re is ft, wht re its length nd width? Define Length= Width= Eqution : Eqution :
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