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Sisa pembagian suku banyak oleh adalah . Nilai adalah... (UN 2015)

Sisa pembagian suku banyak begin mathsize 14px style f left parenthesis x right parenthesis equals x cubed minus 3 x squared plus p x plus q end style oleh begin mathsize 14px style open parentheses x squared plus x minus 2 close parentheses end style adalah begin mathsize 14px style 2 x minus 3 end style. Nilai begin mathsize 14px style p minus q space end style adalah... (UN 2015)

  1. begin mathsize 14px style negative 15 end style

  2. begin mathsize 14px style negative 9 end style

  3. begin mathsize 14px style 7 end style

  4. begin mathsize 14px style 9 end style

  5. begin mathsize 14px style 15 end style

Jawaban:

Pertama kita menetukan faktor dari begin mathsize 14px style open parentheses x squared plus x minus 2 close parentheses end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x squared plus x minus 2 end cell row blank blank cell open parentheses x plus 2 close parentheses open parentheses x minus 1 close parentheses end cell row x equals cell negative 2 space atau space x equals 1 end cell end table end style

Jika suku banyak begin mathsize 11px style f left parenthesis x right parenthesis end style dibagi oleh begin mathsize 14px style left parenthesis x plus 2 right parenthesis left parenthesis x minus 1 right parenthesis end style  bersisa begin mathsize 14px style 2 x minus 3 end style maka untukbegin mathsize 14px style space x equals negative 2 space dan space x equals 1 space end style nilai suku banyak tersebut adalah begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 3 end style 

untuk begin mathsize 14px style x equals 1 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x cubed minus 3 x squared plus p x plus q end cell row cell f left parenthesis 1 right parenthesis end cell equals cell open parentheses 1 close parentheses cubed minus 3 open parentheses 1 close parentheses squared plus p open parentheses 1 close parentheses plus q end cell row cell 2 open parentheses 1 close parentheses minus 3 end cell equals cell 1 minus 3 plus p plus q end cell row cell 2 minus 3 end cell equals cell negative 2 plus p plus q end cell row cell p plus q end cell equals cell 1... open parentheses 1 close parentheses end cell row blank blank blank end table end style

Untuk begin mathsize 14px style x equals negative 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x cubed minus 3 x squared plus p x plus q end cell row cell f left parenthesis negative 2 right parenthesis end cell equals cell open parentheses negative 2 close parentheses cubed minus 3 open parentheses negative 2 close parentheses squared plus p open parentheses negative 2 close parentheses plus q end cell row cell 2 open parentheses negative 2 close parentheses minus 3 end cell equals cell negative 8 minus 12 minus 2 p plus q end cell row cell negative 4 minus 3 end cell equals cell negative 20 minus 2 p plus q end cell row cell negative 2 p plus q end cell equals cell 13... open parentheses 2 close parentheses end cell row blank blank blank end table end style

Kemudian eliminasi persamaan 1 dan 2

begin mathsize 14px style table row cell p plus q equals 1 end cell row cell negative 2 p plus q equals 13 end cell row cell 3 p equals negative 12 end cell row cell p equals negative 4 end cell end table minus end style

Subtitusi nilai P ke persamaan (1)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p plus q end cell equals cell 1 ` end cell row cell negative 4 plus q end cell equals 1 row q equals 5 end table end style

Maka begin mathsize 14px style p minus q equals open parentheses negative 4 close parentheses minus open parentheses 5 close parentheses equals negative 9 end style

Jadi, jawaban yang tepat adalah B

 

 

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