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Sisa pembagian polinomial oleh  adalah . Nilai  adalah ...

Pertanyaan

Sisa pembagian polinomial begin mathsize 14px style p left parenthesis x right parenthesis equals x cubed plus a x squared minus 4 x plus b space end styleoleh begin mathsize 14px style left parenthesis x squared minus 3 x plus 2 right parenthesis end style adalah begin mathsize 14px style 9 x minus 5 end style. Nilai begin mathsize 14px style a minus b end style adalah ...

  1. begin mathsize 14px style negative 3 end style 

  2. begin mathsize 14px style negative 2 end style 

  3. undefined  

  4. begin mathsize 14px style 2 end style 

  5. begin mathsize 14px style 3 end style 

Pembahasan Video:

Pembahasan Soal:

Ingat: size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px p size 14px left parenthesis size 14px x size 14px right parenthesis size 14px times size 14px h begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px s size 14px left parenthesis size 14px x size 14px right parenthesis.

Polinomial begin mathsize 14px style x cubed plus a x squared minus 4 x plus b end style dibagi begin mathsize 14px style x squared minus 3 x plus 2 end style  bersisa begin mathsize 14px style 9 x minus 5 end style
Maka polinomial tersebut dapat didefinisikan :

begin mathsize 14px style f left parenthesis x right parenthesis equals left parenthesis x squared minus 3 x plus 2 right parenthesis times h left parenthesis x right parenthesis plus left parenthesis 9 x minus 5 right parenthesis end style

Pembaginya dapat dijabarkan menjadi begin mathsize 14px style x squared minus 3 x plus 2 equals left parenthesis x minus 2 right parenthesis left parenthesis x minus 1 right parenthesis end style

Untuk begin mathsize 14px style x equals 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 2 right parenthesis end cell equals cell left parenthesis 2 squared plus 2 times 2 minus 8 right parenthesis times h open parentheses x close parentheses plus 9 times 2 minus 5 end cell row cell 2 cubed plus a times 2 squared minus 4 times 2 plus b end cell equals cell 0 times h open parentheses 2 close parentheses plus 13 end cell row cell 4 a plus b end cell equals cell 13 space end cell row b equals cell 13 minus 4 a space horizontal ellipsis space pers left parenthesis 1 right parenthesis end cell row blank blank blank end table end style

Untuk begin mathsize 14px style x equals 1 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 1 right parenthesis end cell equals cell left parenthesis 1 squared plus 2 times 1 minus 8 right parenthesis times h left parenthesis 1 right parenthesis plus 9 times 1 minus 5 end cell row cell 1 cubed plus a times 1 squared minus 4 times 1 plus b end cell equals cell 0 times h left parenthesis 1 right parenthesis plus 4 end cell row cell a plus b end cell equals cell 4 plus 3 space end cell row cell a plus b end cell equals cell 7 space horizontal ellipsis space pers left parenthesis 2 right parenthesis end cell row blank blank blank end table end style

Substitusikan pers (1) ke pers (2)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus 13 minus 4 a end cell equals 7 row cell negative 3 a end cell equals cell negative 6 end cell row a equals 2 row cell Maka space straight b end cell equals cell 13 minus 4 times 2 equals 5 end cell end table end style

Sehingga begin mathsize 14px style a minus b equals 2 minus 5 equals negative 3 end style

Jadi, Jawaban yang tepat adalah A

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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