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Diketahui sisa pembagian polinomial  oleh  dan  berturut-turut  dan . Tentukan sisa pembagian polinomial  oleh .

Pertanyaan

Diketahui sisa pembagian polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style oleh begin mathsize 14px style left parenthesis 2 x plus 3 right parenthesis end style dan begin mathsize 14px style left parenthesis 3 x minus 2 right parenthesis end style berturut-turut begin mathsize 14px style negative 3 end style dan begin mathsize 14px style 7 end style. Tentukan sisa pembagian polinomial undefined oleh begin mathsize 14px style left parenthesis 6 x squared plus 5 x minus 6 right parenthesis end style.

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Pembahasan Video:

Pembahasan Soal:

  • Polinomialnya begin mathsize 14px style straight p left parenthesis straight x right parenthesis end style dibagi begin mathsize 14px style 2 x plus 3 end style sisa begin mathsize 14px style negative 3 end style atau bisa ditulis  begin mathsize 14px style p open parentheses negative 3 over 2 close parentheses equals negative 3 end style
  • Polinomial undefined dibagi begin mathsize 14px style open parentheses 3 x minus 2 close parentheses end style sisa 7 atau bisa ditulis begin mathsize 14px style p open parentheses 2 over 3 close parentheses equals 7 end style 
  • Polinomial undefined dibagi begin mathsize 14px style open parentheses 6 x squared plus 5 x minus 6 close parentheses end style atau bisa dijabarkan begin mathsize 14px style 6 x squared plus 5 x minus 6 equals open parentheses 2 x plus 3 close parentheses open parentheses 3 x minus 2 close parentheses end style   

Ingat: Jika polinomial undefined dibagi begin mathsize 14px style left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis end style, maka sisanya begin mathsize 14px style straight s left parenthesis straight x right parenthesis equals fraction numerator straight p left parenthesis straight a right parenthesis minus straight p left parenthesis straight b right parenthesis over denominator straight a minus straight b end fraction straight x plus fraction numerator straight a times straight f left parenthesis straight b right parenthesis minus straight b times straight f left parenthesis straight a right parenthesis over denominator straight a minus straight b end fraction end style

sehingga sisa pembagian  undefined oleh begin mathsize 14px style open parentheses 2 x plus 3 close parentheses open parentheses 3 x minus 2 close parentheses end style adalah

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight s left parenthesis straight x right parenthesis end cell equals cell fraction numerator straight p open parentheses negative begin display style 3 over 2 end style close parentheses minus straight p open parentheses begin display style 2 over 3 end style close parentheses over denominator negative begin display style 3 over 2 end style minus begin display style 2 over 3 end style end fraction straight x plus fraction numerator negative 3 over 2 times straight p open parentheses begin display style 2 over 3 end style close parentheses minus 2 over 3 times p open parentheses begin display style fraction numerator negative 3 over denominator 2 end fraction end style close parentheses over denominator negative 3 over 2 minus 2 over 3 end fraction end cell row blank equals cell fraction numerator open parentheses negative 3 close parentheses minus 7 over denominator begin display style fraction numerator negative 9 minus 4 over denominator 6 end fraction end style end fraction x plus fraction numerator open parentheses negative 3 over 2 times 7 close parentheses minus open parentheses 2 over 3 times negative 3 close parentheses over denominator fraction numerator negative 9 minus 4 over denominator 6 end fraction end fraction end cell row blank equals cell fraction numerator 6 times open parentheses negative 10 close parentheses over denominator negative 13 end fraction x plus fraction numerator 6 open parentheses begin display style fraction numerator negative 21 over denominator 2 end fraction end style plus 2 close parentheses over denominator negative 13 end fraction end cell row blank equals cell 60 over 13 x plus 51 over 13 end cell end table end style  

Jadi sisa pembagian undefined  oleh undefined  adalah begin mathsize 14px style 60 over 13 x plus 51 over 13 end style  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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