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Polinomial  dibagi  bersisa  dan dibagi  bersisa . Tentukan sisa pembagian polinomial  oleh .

Pertanyaan

Polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style dibagi begin mathsize 14px style x squared minus 4 end style bersisa begin mathsize 14px style 3 x minus 6 end style dan dibagi begin mathsize 14px style x squared plus 2 x minus 15 end style bersisa begin mathsize 14px style 4 x plus 6 end style. Tentukan sisa pembagian polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style oleh begin mathsize 14px style x squared minus x minus 6 end style

  1. ...space 

  2. ... undefined 

Pembahasan Video:

Pembahasan Soal:

Polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style dibagi begin mathsize 14px style x squared minus 4 end style bersisa begin mathsize 14px style 3 x minus 6 end style,

begin mathsize 14px style x squared minus 4 equals left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis end style, maka

begin mathsize 14px style p left parenthesis negative 2 right parenthesis equals 3 left parenthesis negative 2 right parenthesis minus 6 equals negative 6 minus 6 equals negative 12 p left parenthesis 2 right parenthesis equals 3 left parenthesis 2 right parenthesis minus 6 equals 6 minus 6 equals 0 end style 

Polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style dibagi begin mathsize 14px style x squared plus 2 x minus 15 end style bersisa begin mathsize 14px style 4 x plus 6 end style,

begin mathsize 14px style x squared plus 2 x minus 15 equals left parenthesis x minus 3 right parenthesis left parenthesis x plus 5 right parenthesis end style, maka

begin mathsize 14px style p left parenthesis 3 right parenthesis equals 4 left parenthesis 3 right parenthesis plus 6 equals 12 plus 6 equals 18 p left parenthesis negative 5 right parenthesis equals 4 left parenthesis negative 5 right parenthesis plus 6 equals negative 20 plus 6 equals negative 14 end style

Sisa pembagian polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style oleh begin mathsize 14px style x squared minus x minus 6 end style,

Pembagi: begin mathsize 14px style x squared minus x minus 6 equals left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis end style

Karena pembagi berderajat 2 maka sisa pembagian nya berderajat 1, misalkan begin mathsize 14px style a x plus b end style.

begin mathsize 14px style p left parenthesis x right parenthesis end style dibagi begin mathsize 14px style left parenthesis x minus 3 right parenthesis end style memiliki sisa, 

begin mathsize 14px style p left parenthesis 3 right parenthesis equals 18 rightwards double arrow 3 a plus b equals 18 space space space space space space space space space space space space space space left right double arrow b equals 18 minus 3 a space... left parenthesis 1 right parenthesis end style

undefined dibagi begin mathsize 14px style left parenthesis x plus 2 right parenthesis end style memiliki sisa,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis negative 2 right parenthesis end cell equals cell negative 12 end cell row cell negative 2 a plus b end cell equals cell negative 12 end cell row b equals cell 2 a minus 12 horizontal ellipsis left parenthesis 2 right parenthesis end cell end table end style 

Dari persamaan (1) dan (2), diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 3 a plus 18 end cell equals cell 2 a minus 12 end cell row cell negative 5 a end cell equals cell negative 30 end cell row a equals 6 end table end style 

Substitusi table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px a end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 6 end table  ke persamaaan (1)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row b equals cell negative 3 a plus 18 end cell row blank equals cell negative 3 left parenthesis 6 right parenthesis plus 18 end cell row blank equals cell negative 18 plus 18 end cell row blank equals 0 end table end style 

 Diperoleh sisa pembagian undefined oleh begin mathsize 14px style x squared minus x minus 6 end style adalah begin mathsize 14px style 6 x end style .

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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