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Suku banyak  jika dibagi  bersisa . Diketahui pula suku banyak . Apabila  dibagi  akan bersisa …

Pertanyaan

Suku banyak begin mathsize 14px style P left parenthesis x right parenthesis end style jika dibagi begin mathsize 14px style x squared minus 5 x plus 6 end style bersisa begin mathsize 14px style 6 minus x end style. Diketahui pula suku banyak begin mathsize 14px style Q left parenthesis x right parenthesis equals left parenthesis x minus 2 right parenthesis to the power of 2019 plus left parenthesis x minus 3 right parenthesis to the power of 2018 – 2 x plus 2 end style. Apabila begin mathsize 14px style P left parenthesis x right parenthesis. Q left parenthesis x right parenthesis end style dibagi undefined akan bersisa …

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

  2. begin mathsize 14px style negative 6 x plus 5 end style 

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

  4. begin mathsize 14px style negative 5 x plus 6 end style 

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

Pembahasan Soal:

Suku banyak begin mathsize 14px style P left parenthesis x right parenthesis end style jika dibagi begin mathsize 14px style x squared minus 5 x plus 6 end style bersisa begin mathsize 14px style 6 minus x end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis x right parenthesis end cell equals cell left parenthesis x squared minus 5 x plus 6 right parenthesis h subscript 1 left parenthesis x right parenthesis plus 6 minus x end cell row cell P left parenthesis x right parenthesis end cell equals cell left parenthesis x minus 3 right parenthesis left parenthesis x minus 2 right parenthesis h subscript 1 left parenthesis x right parenthesis plus 6 minus x end cell row cell P left parenthesis 3 right parenthesis end cell equals cell left parenthesis 3 minus 3 right parenthesis left parenthesis 3 minus 2 right parenthesis h subscript 1 left parenthesis 3 right parenthesis plus 6 minus 3 end cell row cell P left parenthesis 3 right parenthesis end cell equals 3 row blank blank blank row cell P left parenthesis 2 right parenthesis end cell equals cell left parenthesis 2 minus 3 right parenthesis left parenthesis 2 minus 2 right parenthesis h subscript 1 left parenthesis 2 right parenthesis plus 6 minus 2 end cell row cell P left parenthesis 2 right parenthesis end cell equals 4 row blank blank blank row cell Q left parenthesis x right parenthesis end cell equals cell left parenthesis x minus 2 right parenthesis to the power of 2019 plus left parenthesis x minus 3 right parenthesis to the power of 2018 – 2 x plus 2 end cell row cell Q left parenthesis 3 right parenthesis end cell equals cell left parenthesis 3 minus 2 right parenthesis to the power of 2019 plus left parenthesis 3 minus 3 right parenthesis to the power of 2018 – 2 left parenthesis 3 right parenthesis plus 2 end cell row cell Q left parenthesis 3 right parenthesis end cell equals cell 1 to the power of 2019 plus 0 minus 6 plus 2 end cell row cell Q left parenthesis 3 right parenthesis end cell equals cell 1 minus 4 end cell row cell Q left parenthesis 3 right parenthesis end cell equals cell negative 3 end cell row blank blank blank row cell Q left parenthesis 2 right parenthesis end cell equals cell left parenthesis 2 minus 2 right parenthesis to the power of 2019 plus left parenthesis 2 minus 3 right parenthesis to the power of 2018 – 2 left parenthesis 2 right parenthesis plus 2 end cell row cell Q left parenthesis 2 right parenthesis end cell equals cell 0 plus left parenthesis negative 1 right parenthesis to the power of 2018 minus 4 plus 2 end cell row cell Q left parenthesis 2 right parenthesis end cell equals cell 1 minus 2 end cell row cell Q left parenthesis 2 right parenthesis end cell equals cell negative 1 end cell end table end style

begin mathsize 14px style P left parenthesis x right parenthesis. Q left parenthesis x right parenthesis end style dibagi undefined akan memiliki sisa berderajat 1, karena pembaginya berderajat 2, maka dapat kita misalkan sisa yang akan dihasilkan dengan bentuk begin mathsize 14px style p x plus q end style. Sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis x right parenthesis. Q left parenthesis x right parenthesis end cell equals cell left parenthesis x squared minus 5 x plus 6 right parenthesis h subscript 3 left parenthesis x right parenthesis plus p x plus q end cell row cell P left parenthesis x right parenthesis. Q left parenthesis x right parenthesis end cell equals cell left parenthesis x minus 3 right parenthesis left parenthesis x minus 2 right parenthesis h subscript 3 left parenthesis x right parenthesis plus p x plus q end cell row cell P left parenthesis 2 right parenthesis. Q left parenthesis 2 right parenthesis end cell equals cell left parenthesis 2 minus 3 right parenthesis left parenthesis 2 minus 2 right parenthesis h subscript 3 left parenthesis 2 right parenthesis plus p left parenthesis 2 right parenthesis plus q end cell row cell left parenthesis 4 right parenthesis left parenthesis negative 1 right parenthesis end cell equals cell 0 plus 2 p plus q end cell row cell 2 p plus q end cell equals cell negative 4 space........................ space left parenthesis 1 right parenthesis end cell row blank blank blank row cell P left parenthesis 3 right parenthesis. Q left parenthesis 3 right parenthesis end cell equals cell left parenthesis 3 minus 3 right parenthesis left parenthesis 3 minus 2 right parenthesis h subscript 3 left parenthesis 3 right parenthesis plus p left parenthesis 3 right parenthesis plus q end cell row cell left parenthesis 3 right parenthesis left parenthesis negative 3 right parenthesis end cell equals cell 0 plus 3 p plus q end cell row cell 3 p plus q end cell equals cell negative 9 space........................ space left parenthesis 2 right parenthesis end cell end table end style 

Eliminasi (1) dan (2), maka:

begin mathsize 14px style table row cell 2 p plus q equals negative 4 end cell row cell 3 p plus q equals negative 9 end cell row cell negative p equals 5 end cell row cell p equals negative 5 end cell end table minus end style  

Untuk menentukan nilai begin mathsize 14px style q end style kita substitusikan nilai begin mathsize 14px style p equals negative 5 end style ke sala satu persamaan yaitu begin mathsize 14px style 2 p plus q equals negative 4 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p plus q end cell equals cell negative 4 end cell row cell 2 left parenthesis negative 5 right parenthesis plus q end cell equals cell negative 4 end cell row cell negative 10 plus q end cell equals cell negative 4 end cell row q equals cell negative 4 plus 10 end cell row q equals 6 end table end style 

Maka sisa begin mathsize 14px style P left parenthesis x right parenthesis. Q left parenthesis x right parenthesis end style dibagi undefined adalah begin mathsize 14px style negative 5 x plus 6 end style.

Jadi, jawabanyang tepat adalah D

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

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