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Suku banyak begin mathsize 14px style P open parentheses x close parentheses end style dibagi begin mathsize 14px style open parentheses 2 x minus 1 close parentheses end style dan dibagi begin mathsize 14px style open parentheses 3 x plus 2 close parentheses end style berturut turut bersisa begin mathsize 14px style 2 end style dan begin mathsize 14px style negative 3 end style. suku banyak undefined dibagi oleh undefined dan undefined berturut turut bersisa begin mathsize 14px style negative 2 end style dan begin mathsize 14px style 6 end style. Sisa pembagian suku banyak begin mathsize 14px style h open parentheses x close parentheses equals p open parentheses x close parentheses times f open parentheses x close parentheses end style oleh begin mathsize 14px style open parentheses 2 x minus 1 close parentheses open parentheses 3 x plus 2 close parentheses end style adalah .... 

  1. begin mathsize 14px style 12 x plus 10 end style   

  2. begin mathsize 14px style 12 x minus 10 end style   

  3. begin mathsize 14px style 6 x plus 5 end style   

  4. begin mathsize 14px style 5 x minus 5 end style   

  5. begin mathsize 14px style 12 x minus 6 end style   

Jawaban:

1. Suku banyak begin mathsize 14px style P open parentheses x close parentheses end style dibagi begin mathsize 14px style open parentheses 2 x minus 1 close parentheses end style dan dibagi begin mathsize 14px style open parentheses 3 x plus 2 close parentheses end style berturut turut bersisa begin mathsize 14px style 2 end style dan begin mathsize 14px style negative 3 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight p open parentheses straight x close parentheses space colon space open parentheses 2 straight x minus 1 close parentheses end cell rightwards arrow cell sisa space 2 end cell row cell 2 straight x minus 1 end cell equals 0 row cell 2 straight x end cell equals 1 row straight x equals cell 1 half end cell row maka colon blank row cell straight p open parentheses 1 half close parentheses end cell equals 2 row blank blank blank row cell straight p open parentheses straight x close parentheses space colon space open parentheses 3 straight x plus 2 close parentheses end cell rightwards arrow cell sisa space minus 3 end cell row cell 3 straight x plus 2 end cell equals 0 row cell 3 straight x end cell equals cell negative 2 end cell row straight x equals cell negative 2 over 3 end cell row maka colon blank row cell straight p open parentheses negative 2 over 3 close parentheses end cell equals cell negative 3 end cell end table end style 
 

2. Suku banyak undefined dibagi oleh undefined dan undefined berturut turut bersisa begin mathsize 14px style negative 2 end style dan begin mathsize 14px style 6 end style
 

undefined 

3. Sisa pembagian suku banyak begin mathsize 14px style h open parentheses x close parentheses equals p open parentheses x close parentheses times f open parentheses x close parentheses end style oleh begin mathsize 14px style open parentheses 2 x minus 1 close parentheses open parentheses 3 x plus 2 close parentheses end style dimisalkan begin mathsize 14px style straight S open parentheses straight x close parentheses equals ax plus straight b end style , dapat dituliskan sebagai
 

undefined 
 

Selanjutnya kita masukkan nilai yang sudah kita ketahui sebelumnya, yaitu begin mathsize 14px style straight x equals 1 half end style, sehingga persamaannya menjadi :

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight p left parenthesis straight x right parenthesis times straight f left parenthesis straight x right parenthesis end cell equals cell straight S left parenthesis straight x right parenthesis equals ax plus straight b end cell row cell straight p left parenthesis 1 half right parenthesis times straight f left parenthesis 1 half right parenthesis times end cell equals cell left parenthesis 1 half straight a plus straight b right parenthesis end cell row cell 2 times left parenthesis negative 2 right parenthesis end cell equals cell 1 half straight a plus straight b end cell row cell negative 4 end cell equals cell 1 half straight a plus straight b end cell row cell negative 8 end cell equals cell straight a plus 2 straight b end cell row straight a equals cell negative 8 minus 2 straight b... left parenthesis pers. space 1 right parenthesis end cell end table end style     
 

Selanjutnya kita masukkan nilai yang sudah kita ketahui sebelumnya, yaitu begin mathsize 14px style straight x equals negative 2 over 3 end style, sehingga persamaannya menjadi :
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight p open parentheses straight x close parentheses times straight f open parentheses straight x close parentheses end cell equals cell straight S open parentheses straight x close parentheses equals ax plus straight b end cell row cell straight p open parentheses negative 2 over 3 close parentheses times straight f open parentheses negative 2 over 3 close parentheses end cell equals cell open parentheses negative 2 over 3 straight a plus straight b close parentheses end cell row cell negative 3 times 6 end cell equals cell negative 2 over 3 straight a plus straight b end cell row cell negative 18 end cell equals cell negative 2 over 3 straight a plus straight b end cell row 54 equals cell 2 straight a minus 3 straight b... open parentheses pers. space 2 close parentheses end cell end table end style  
 

Selanjutnya pers. 1 disubstitusikan ke pers. 2
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row 54 equals cell 2 straight a minus 3 straight b end cell row 54 equals cell 2 open parentheses negative 8 minus 2 straight b close parentheses minus 3 straight b end cell row 54 equals cell negative 16 minus 4 straight b minus 3 straight b end cell row cell 7 straight b end cell equals cell negative 70 end cell row straight b equals cell negative 10 end cell end table end style 
 

Nilai begin mathsize 14px style straight b equals negative 10 end style disubstitusikan ke pers. 1
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row straight a equals cell negative 8 minus 2 straight b end cell row blank equals cell negative 8 minus 2 open parentheses negative 10 close parentheses end cell row blank equals cell negative 8 plus 20 end cell row blank cell equals 1 end cell 2 end table end style 
 

Sehingga Sisa pembagian suku banyak begin mathsize 14px style h open parentheses x close parentheses equals p open parentheses x close parentheses times f open parentheses x close parentheses end style oleh begin mathsize 14px style open parentheses 2 x minus 1 close parentheses open parentheses 3 x plus 2 close parentheses end style adalah begin mathsize 14px style straight S open parentheses straight x close parentheses equals ax plus straight b equals 12 straight x minus 10 end style  

Jadi, jawban yang tepat adalah B

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