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Jika suku banyak dibagi  bersisa , tentukan nilai dan !

Pertanyaan

Jika suku banyak f left parenthesis x right parenthesis equals x to the power of 5 plus x to the power of 4 plus p x cubed minus 2 x squared plus left parenthesis 3 q plus 1 right parenthesis x plus 3 dibagi open parentheses x squared plus x minus 2 close parentheses bersisa 2 straight x plus 9, tentukan nilai p dan q!

Pembahasan Soal:

Teorema sisa pada suku banyak

Jika suku banyak f left parenthesis x right parenthesis equals x to the power of 5 plus x to the power of 4 plus p x cubed minus 2 x squared plus left parenthesis 3 q plus 1 right parenthesis x plus 3 dibagi open parentheses x squared plus x minus 2 close parentheses bersisa 2 straight x plus 9.

open parentheses x squared plus x minus 2 close parentheses equals open parentheses x plus 2 close parentheses open parentheses x minus 1 close parentheses

  • Jika suku banyak f left parenthesis x right parenthesis equals x to the power of 5 plus x to the power of 4 plus p x cubed minus 2 x squared plus left parenthesis 3 q plus 1 right parenthesis x plus 3 dibagi open parentheses x plus 2 close parentheses diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 2 right parenthesis end cell equals cell open parentheses negative 2 close parentheses to the power of 5 plus open parentheses negative 2 close parentheses to the power of 4 plus p open parentheses negative 2 close parentheses cubed minus 2 open parentheses negative 2 close parentheses squared plus left parenthesis 3 q plus 1 right parenthesis open parentheses negative 2 close parentheses plus 3 end cell row cell 2 open parentheses negative 2 close parentheses plus 9 end cell equals cell open parentheses negative 2 close parentheses to the power of 5 plus open parentheses negative 2 close parentheses to the power of 4 plus p open parentheses negative 2 close parentheses cubed minus 2 open parentheses negative 2 close parentheses squared plus left parenthesis 3 q plus 1 right parenthesis open parentheses negative 2 close parentheses plus 3 end cell row cell negative 4 plus 9 end cell equals cell negative 32 plus 16 minus 8 p minus 8 minus 6 q minus 2 plus 3 end cell row 5 equals cell negative 23 minus 8 p minus 6 q end cell row cell 5 plus 23 end cell equals cell negative 8 p minus 6 q end cell row 28 equals cell negative 8 p minus 6 q end cell row 14 equals cell negative 4 p minus 3 q end cell end table

  • Jika suku banyak f left parenthesis x right parenthesis equals x to the power of 5 plus x to the power of 4 plus p x cubed minus 2 x squared plus left parenthesis 3 q plus 1 right parenthesis x plus 3 dibagi open parentheses x minus 1 close parentheses diperoleh

space space space space space space f left parenthesis 1 right parenthesis equals left parenthesis 1 right parenthesis to the power of 5 plus left parenthesis 1 right parenthesis to the power of 4 plus p left parenthesis 1 right parenthesis cubed minus 2 left parenthesis 1 right parenthesis squared plus left parenthesis 3 q plus 1 right parenthesis left parenthesis 1 right parenthesis plus 3 2 left parenthesis 1 right parenthesis plus 9 equals 1 plus 1 plus p minus 2 plus 3 q plus 1 plus 3 space space space space space space space 11 space equals p plus 3 q plus 4 space space space space space space space space space 7 space equals space p plus 3 q

Eliminasi dan subtitusi persamaan-persamaan diatas. Sehingga diperoleh

14 equals negative 4 p minus 3 q space bottom enclose space 7 equals space space space space space p plus 3 q end enclose space space plus space 21 equals space minus 3 p space space space p equals space minus 7

Untuk p equals negative 7, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row 7 equals cell p plus 3 q end cell row 7 equals cell negative 7 plus 3 q end cell row 14 equals cell 3 q end cell row cell 3 q end cell equals cell 14 space end cell row q equals cell 14 over 3 end cell end table

Jadi, nilai p dan q adalah p equals negative 7 dan q equals 14 over 3.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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