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Diketahui polinomial . Jika  dibagi  sisa 11, dibagi  sisa , nilai  adalah ... .

Pertanyaan

Diketahui polinomial begin mathsize 14px style p left parenthesis x right parenthesis equals 2 x to the power of 4 plus a x cubed minus 3 x squared plus 5 x plus b end style. Jika undefined dibagi begin mathsize 14px style left parenthesis x minus 1 right parenthesis end style sisa 11, dibagi begin mathsize 14px style left parenthesis x plus 1 right parenthesis end style sisa undefined, nilai begin mathsize 14px style left parenthesis 2 a plus b right parenthesis end style adalah ... .

  1. 13undefined 

  2. 10undefined 

  3. 8undefined  

  4. 7undefined  

  5. 6undefined  

Pembahasan Video:

Pembahasan Soal:

Polinomial begin mathsize 14px style p left parenthesis x right parenthesis equals 2 x to the power of 4 plus a x cubed minus 3 x squared plus 5 x plus b end style. Jika undefined dibagi begin mathsize 14px style left parenthesis x minus 1 right parenthesis end style sisa 11,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis 1 right parenthesis end cell equals 11 row cell 2 left parenthesis 1 right parenthesis to the power of 4 plus a left parenthesis 1 right parenthesis cubed minus 3 left parenthesis 1 right parenthesis squared plus 5 left parenthesis 1 right parenthesis plus b end cell equals 11 row cell 2 plus a minus 3 plus 5 plus b end cell equals 11 row cell a plus b end cell equals cell 7 space space space... left parenthesis 1 right parenthesis end cell end table end style 

Jika begin mathsize 14px style p left parenthesis x right parenthesis end style dibagi begin mathsize 14px style left parenthesis x plus 1 right parenthesis end style sisa undefined,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis negative 1 right parenthesis end cell equals cell negative 1 end cell row cell 2 left parenthesis negative 1 right parenthesis to the power of 4 plus a left parenthesis negative 1 right parenthesis cubed minus 3 left parenthesis negative 1 right parenthesis squared plus 5 left parenthesis negative 1 right parenthesis plus b end cell equals cell negative 1 end cell row cell 2 minus a minus 3 minus 5 plus b end cell equals cell negative 1 end cell row cell negative a plus b end cell equals cell 5 space space space space... left parenthesis 2 right parenthesis end cell end table end style 

Eliminasi persamaan begin mathsize 14px style left parenthesis 1 right parenthesis end style dan persamaan begin mathsize 14px style left parenthesis 2 right parenthesis end style,

 

Subtitusi nilai undefined ke persamaan begin mathsize 14px style left parenthesis 1 right parenthesis end style ,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 1 plus b end cell equals 7 row cell space space space space space b end cell equals 6 end table end style 

Selanjutnya mencari  nilai begin mathsize 14px style 2 a plus b end style dengan mensubtitusi undefined dan begin mathsize 14px style b equals 6 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a plus b end cell equals cell 2 left parenthesis 1 right parenthesis plus 6 end cell row blank equals 8 end table end style

Dengan demikian diperoleh nilai begin mathsize 14px style 2 a plus b equals 8 end style.

Jadi, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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