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Polinomial  habis dibagi oleh . Jika  dibagi  sisanya , tentukan nilai  dan .

Pertanyaan

Polinomial begin mathsize 14px style f left parenthesis x right parenthesis equals x cubed minus left parenthesis a minus 1 right parenthesis x squared plus b x plus 2 a end style habis dibagi oleh begin mathsize 14px style left parenthesis x plus 2 right parenthesis end style. Jika begin mathsize 14px style f left parenthesis x right parenthesis end style dibagi begin mathsize 14px style left parenthesis x minus 2 right parenthesis end style sisanya begin mathsize 14px style negative 4 end style, tentukan nilai undefined dan begin mathsize 14px style b end style

  1. undefined 

  2. undefined 

Pembahasan Video:

Pembahasan Soal:

Jika begin mathsize 14px style f left parenthesis x right parenthesis end style habis dibagi begin mathsize 14px style open parentheses x plus 2 close parentheses end style artinya sisa = 0, maka:

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 left parenthesis a minus 1 right parenthesis x squared plus b x plus 2 a end cell row cell f left parenthesis negative 2 right parenthesis end cell equals cell left parenthesis negative 2 right parenthesis cubed minus left parenthesis a minus 1 right parenthesis times left parenthesis negative 2 right parenthesis squared plus b times left parenthesis negative 2 right parenthesis plus 2 a end cell row 0 equals cell negative 8 minus 4 a plus 4 minus 2 b plus 2 a end cell row 0 equals cell negative 4 minus 2 a minus 2 b end cell row 4 equals cell negative 2 a minus 2 b space... left parenthesis straight I right parenthesis end cell end table end style 

Jika begin mathsize 14px style f left parenthesis x right parenthesis end style dibagi begin mathsize 14px style left parenthesis x minus 2 right parenthesis end style sisanya begin mathsize 14px style negative 4 end style, maka:

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 left parenthesis a minus 1 right parenthesis x squared plus b x plus 2 a end cell row cell f left parenthesis 2 right parenthesis end cell equals cell left parenthesis 2 right parenthesis cubed minus left parenthesis a minus 1 right parenthesis times left parenthesis 2 right parenthesis squared plus b times left parenthesis 2 right parenthesis plus 2 a end cell row cell negative 4 end cell equals cell 8 minus 4 a plus 4 plus 2 b plus 2 a end cell row cell negative 4 end cell equals cell 12 minus 2 a plus 2 b end cell row cell negative 16 end cell equals cell negative 2 a plus 2 b space... left parenthesis II right parenthesis end cell end table end style 

Gunakan metode eliminasi dan subtitusi pada persamaan I dan II untuk mencari nilai undefined dan begin mathsize 14px style b end style.

begin mathsize 14px style negative 2 a minus 2 b equals 4 bottom enclose negative 2 a plus 2 b equals negative 16 end enclose space _ minus 4 a space space space space space space space space space equals negative 12 space space space space space space space space space space space space space space space a equals 3 end style

lalu substitusi ke

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 a plus 2 b end cell equals cell negative 16 end cell row cell negative 2 times 3 plus 2 b end cell equals cell negative 16 end cell row cell negative 6 plus 2 b end cell equals cell negative 16 end cell row cell 2 b end cell equals cell negative 10 end cell row b equals cell negative 5 end cell end table end style  

Jadi, nilai 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 3 end table dan begin mathsize 14px style b equals negative 5 end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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