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Polinomial  merupakan hasil perkalian dari  dan  yaitu: Nilai polinomial  untuk  ditentukan dengan cara skema Horner sebagai berikut. Diperoleh nilai

Pertanyaan

Polinomial begin mathsize 14px style k left parenthesis x right parenthesis end style merupakan hasil perkalian dari begin mathsize 14px style f left parenthesis x right parenthesis end style dan begin mathsize 14px style g left parenthesis x right parenthesis end style yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell k left parenthesis x right parenthesis space end cell equals cell space f left parenthesis x right parenthesis cross times g left parenthesis x right parenthesis end cell row blank equals cell space left parenthesis 3 x cubed minus... plus 6 right parenthesis left parenthesis x squared plus 3 x minus 8 right parenthesis end cell row blank equals cell space 3 x cubed left parenthesis x squared plus 3 x minus 8 right parenthesis minus 2 x squared left parenthesis x squared plus... negative 8 right parenthesis plus 6 left parenthesis x squared plus 3 x minus... right parenthesis end cell row blank equals cell space 3 x to the power of 5 plus 9 x to the power of 4 minus 24 x cubed minus... negative 6 x cubed plus 16 x squared plus 6 x squared plus 18 x minus... end cell row blank equals cell 3 x to the power of 5 plus 9 x to the power of 4 minus 2 x to the power of 4 minus 24 x cubed minus 6 x cubed plus... plus 6 x squared plus... negative 48 end cell row blank equals cell 3 x to the power of 5 plus 7 x to the power of 4 minus... plus 22 x squared plus 18 x minus... end cell end table end style

Nilai polinomial undefined untuk begin mathsize 14px style x equals 2 end style ditentukan dengan cara skema Horner sebagai berikut.

Diperoleh nilai begin mathsize 14px style k left parenthesis 2 right parenthesis equals... end style 

  1. ...space 

  2. ...undefined 

Pembahasan Video:

Pembahasan Soal:

Misalkan: begin mathsize 14px style f open parentheses x close parentheses equals 3 x cubed minus 2 x squared plus 6 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x squared plus 3 x minus 8 end style 

Maka,

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell k left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis cross times g left parenthesis x right parenthesis end cell row cell k left parenthesis x right parenthesis end cell equals cell left parenthesis 3 x cubed minus bold 2 bold italic x to the power of bold 2 plus 6 right parenthesis left parenthesis x squared plus 3 x minus 8 right parenthesis end cell row cell k left parenthesis x right parenthesis end cell equals cell 3 x cubed left parenthesis x squared plus 3 x minus 8 right parenthesis minus 2 x squared left parenthesis x squared plus bold 3 bold italic x minus 8 right parenthesis plus 6 left parenthesis x squared plus 3 x minus bold 8 right parenthesis end cell row cell k left parenthesis x right parenthesis end cell equals cell 3 x to the power of 5 plus 9 x to the power of 4 minus 24 x cubed minus bold 2 x to the power of 4 minus 6 x cubed plus 16 x squared plus 6 x squared plus 18 x minus bold 48 end cell row cell k left parenthesis x right parenthesis end cell equals cell 3 x to the power of 5 plus 9 x to the power of 4 minus 2 x to the power of 4 minus 24 x cubed minus 6 x cubed plus bold 16 bold italic x to the power of bold 2 plus 6 x squared plus bold 18 bold italic x minus 48 end cell row cell k left parenthesis x right parenthesis end cell equals cell 3 x to the power of 5 plus 7 x to the power of 4 bold minus bold 30 x cubed plus 22 x squared plus 18 x minus bold 48 end cell end table end style 

Nilai polinomial begin mathsize 14px style k open parentheses x close parentheses end style untuk begin mathsize 14px style x equals 2 end style ditentukan dengan skema horner:

 

Diperoleh begin mathsize 14px style k open parentheses 2 close parentheses equals 44 end style.

Jadi, jawaban yang benar adalah begin mathsize 14px style bold italic k begin bold style left parenthesis 2 right parenthesis end style bold equals bold 44 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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