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Diketahui polinomial  habis dibagi . Tentukan sisa pembagian polinomial tersebut oleh .

Pertanyaan

Diketahui polinomial begin mathsize 14px style x to the power of 4 minus a x cubed space plus left parenthesis a space minus space 3 right parenthesis x squared plus 3 x plus 2 a end style habis dibagi begin mathsize 14px style left parenthesis x minus 2 right parenthesis end style. Tentukan sisa pembagian polinomial tersebut oleh begin mathsize 14px style x squared plus x minus 6 end style.

  1. begin mathsize 14px style.... end style 

  2. undefined 

Pembahasan Video:

Pembahasan Soal:

Ingat kembali yah jika polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style habis dibagi begin mathsize 14px style left parenthesis x minus k right parenthesis end style, maka sisanya adalah 0 atau undefined.

Polinomial begin mathsize 14px style p left parenthesis x right parenthesis equals x to the power of 4 minus a x cubed plus open parentheses a minus 3 close parentheses x squared plus 3 x plus 2 a end style habis dibagi  begin mathsize 14px style open parentheses x minus 2 close parentheses end style, maka undefined.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis 2 right parenthesis end cell equals 0 row cell left parenthesis 2 right parenthesis to the power of 4 minus a times left parenthesis 2 right parenthesis cubed plus left parenthesis a minus 3 right parenthesis times left parenthesis 2 right parenthesis squared plus 3 times 2 plus 2 a end cell equals 0 row cell 16 minus 8 a plus 4 a minus 12 plus 6 plus 2 a end cell equals 0 row cell negative 2 a plus 10 end cell equals 0 row cell negative 2 a end cell equals cell negative 10 end cell row a equals cell fraction numerator negative 10 over denominator negative 2 end fraction end cell row a equals 5 end table end style 

Polinomialnya menjadi begin mathsize 14px style x to the power of 4 minus 5 x cubed plus 2 x squared plus 3 x plus 10 end style.

Polinomial tersebut dibagi begin mathsize 14px style x squared plus x minus 6 end style atau bisa dijabarkan begin mathsize 14px style x squared plus x minus 6 equals left parenthesis x plus 3 right parenthesis left parenthesis x minus 2 right parenthesis end style 

  • begin mathsize 14px style p left parenthesis 2 right parenthesis equals 0 space end style (habis membagi)
  • begin mathsize 12px style p left parenthesis negative 3 right parenthesis equals left parenthesis negative 3 right parenthesis to the power of 4 minus 5 times left parenthesis negative 3 right parenthesis cubed plus 2 times left parenthesis negative 3 right parenthesis squared plus 3 times left parenthesis negative 3 right parenthesis plus 10 equals 235 end style  

Ingat: Jika polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style 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 s left parenthesis x right parenthesis equals fraction numerator p left parenthesis a right parenthesis minus p left parenthesis b right parenthesis over denominator a minus b end fraction x plus fraction numerator a times p left parenthesis b right parenthesis minus b times p left parenthesis a right parenthesis over denominator a minus b end fraction end style

Oleh karena itu, sisa pembagian undefined oleh begin mathsize 14px style left parenthesis x plus 3 right parenthesis left parenthesis x minus 2 right parenthesis end style adalah begin mathsize 14px style straight s left parenthesis straight x right parenthesis equals fraction numerator straight p left parenthesis negative 3 right parenthesis minus straight p left parenthesis 2 right parenthesis over denominator left parenthesis negative 3 right parenthesis minus 2 end fraction straight x plus fraction numerator negative 3 times p left parenthesis 2 right parenthesis minus 2 times p left parenthesis negative 3 right parenthesis over denominator left parenthesis negative 3 right parenthesis minus 2 end fraction end style

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 left parenthesis negative 3 right parenthesis minus straight p left parenthesis 2 right parenthesis over denominator negative 5 end fraction straight x plus fraction numerator negative 3 times p left parenthesis 2 right parenthesis minus 2 times p left parenthesis negative 3 right parenthesis over denominator negative 5 end fraction end cell row blank equals cell fraction numerator 235 minus 0 over denominator negative 5 end fraction x plus fraction numerator negative 3 times 0 minus 2 times 235 over denominator negative 5 end fraction end cell row blank equals cell negative 47 x plus 94 end cell end table end style  

Jadi, sisa pembagian undefined oleh begin mathsize 14px style open parentheses x squared plus x minus 6 close parentheses end style adalah begin mathsize 14px style negative 47 x plus 94 end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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