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Diketahui polinomial  dan . Jika, tentukan nilai A, B, C, D, dan E.

Pertanyaan

Diketahui polinomial begin mathsize 14px style f left parenthesis space x right parenthesis equals 2 x to the power of 4 plus 5 x cubed minus 3 x squared minus 4 x plus 8 space end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals left parenthesis x squared minus 3 x plus 2 right parenthesis left parenthesis A x squared plus B x plus C right parenthesis plus D x plus E end style. Jikabegin mathsize 14px style f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis end style, tentukan nilai A, B, C, D, dan E.

Pembahasan Video:

Pembahasan Soal:

Diketahui: undefined

Oleh karena itu undefined dapat kita tuliskan sebagai berikut.

begin mathsize 14px style space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis 2 x to the power of 4 plus 5 x cubed minus 3 x squared minus 4 x plus 8 equals left parenthesis x squared minus 3 x plus 2 right parenthesis left parenthesis A x squared plus B x plus C right parenthesis plus D x plus E 2 x to the power of 4 plus 5 x cubed minus 3 x squared minus 4 x plus 8 equals A x to the power of 4 plus B x cubed plus C x squared minus 3 A x cubed minus 3 B x squared minus 3 C x plus 2 A x squared plus 2 B x plus 2 C plus D x plus E 2 x to the power of 4 plus 5 x cubed minus 3 x squared minus 4 x plus 8 equals A x to the power of 4 plus B x cubed minus 3 A x cubed plus C x squared minus 3 B x squared plus 2 A x squared minus 3 C x plus 2 B x plus D x plus 2 C plus E 2 x to the power of 4 plus 5 x cubed minus 3 x squared minus 4 x plus 8 equals A x to the power of 4 plus left parenthesis B minus 3 A right parenthesis x cubed plus left parenthesis C minus 3 B plus 2 A right parenthesis x squared plus left parenthesis negative 3 C plus 2 B plus D right parenthesis x plus left parenthesis 2 C plus E right parenthesis end style 

dari hasil di atas di dapat:

begin mathsize 14px style A equals 2 end style,

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell B minus 3 A end cell equals 5 row cell space space space space space space B minus 3 open parentheses 2 close parentheses end cell equals 5 row cell B minus 6 end cell equals 5 row cell space space space space space space B end cell equals cell 5 plus 6 end cell row B equals 11 end table end style  ,

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell space space space C minus 3 B plus 2 A end cell equals cell negative 3 end cell row cell C minus 3 left parenthesis 11 right parenthesis plus 2 left parenthesis 2 right parenthesis end cell equals cell negative 3 end cell row cell space space space space space space space C minus 33 plus 4 end cell equals cell negative 3 end cell row cell space space space space space space space space space space space space space C minus 29 end cell equals cell negative 3 end cell row cell space space space space space space space space space space space space space space space space space space space space space C end cell equals cell negative 3 plus 29 end cell row cell space space space space space space space space space space space space space space space space space space space space space C end cell equals 26 end table end style  ,

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell space minus 3 C plus 2 B plus D end cell equals cell negative 4 end cell row cell negative 3 open parentheses 26 close parentheses plus 2 left parenthesis 11 right parenthesis plus D end cell equals cell negative 4 end cell row cell space space minus 78 plus 22 plus D end cell equals cell negative 4 end cell row cell space space space space space space space space space space minus 56 plus D end cell equals cell negative 4 end cell row D equals cell negative 4 plus 56 end cell row cell space space space space space space space space space space D end cell equals 52 end table end style  , dan

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell space space space space 2 C plus E end cell equals 8 row cell 2 left parenthesis 26 right parenthesis plus E end cell equals 8 row cell space space space space space 52 plus E end cell equals 8 row cell space space space space space space space space space space space space space E end cell equals cell 8 minus 52 end cell row cell space space space space space space space space space space space space space E end cell equals cell negative 44 end cell end table end style  

Jadi, nilai begin mathsize 14px style A equals 2 comma space B equals 11 comma space C equals 26 comma space D equals 52 end style dan begin mathsize 14px style E equals negative 44 end style 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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