tentukan hasil bagi dan sisa pembagian suku banyak berikut

Leave a Comment / By / July 8, 2022

Tentukan hasil bagi dan sisa dari pembagian suku banyak berikut dengan cara horner.

a. begin mathsize 14px style left parenthesis straight x to the power of 4 minus straight x cubed minus straight x squared plus straight x minus 1 right parenthesis space divided by space left parenthesis straight x squared minus straight x minus 2 right parenthesis end style

Jawaban

Hasil bagi begin mathsize 14px style x squared plus 1 end style dan sisa pembagian begin mathsize 14px style 2 straight x plus 1 end style.

Pembahasan

Teorema faktor dengan metode horner:

Error converting from MathML to accessible text.

Pembagi Error converting from MathML to accessible text.

Horner:

begin mathsize 14px style table row 2 1 cell negative 1 end cell cell negative 1 end cell 1 cell negative 1 end cell row blank vertical ellipsis 2 2 2 cell space space space 6 space plus end cell row cell negative 1 end cell 1 1 1 3 cell space space 5 space space end cell row blank vertical ellipsis cell negative 1 end cell 0 cell negative 1 end cell plus row blank 1 0 1 2 blank end table end style

Hasil bagi: begin mathsize 14px style x squared plus 1 end style.

 

misalkan sisa pembagian begin mathsize 14px style ax plus straight b end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P left parenthesis 2 right parenthesis end cell equals cell 2 straight a plus straight b equals 5 end cell row cell straight P left parenthesis negative 1 right parenthesis end cell equals cell negative straight a plus straight b equals negative 3 end cell end table end style

Dengan eliminasi – substitusi :

begin mathsize 14px style table row cell 2 straight a plus straight b equals 5 end cell row cell negative straight a plus straight b equals negative 1 space minus end cell row cell 3 straight a equals 6 end cell row cell straight a equals 2 end cell row cell negative straight a plus straight b equals negative 1 end cell row cell negative 2 plus straight b equals negative 1 end cell row cell straight b equals 1 end cell end table end style

sisa pembagian begin mathsize 14px style 2 straight x plus 1 end style

Jadi, Hasil bagi begin mathsize 14px style x squared plus 1 end style dan sisa pembagian begin mathsize 14px style 2 straight x plus 1 end style.

Baca juga  panjang sisi ab pada gambar disamping adalah

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