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Tentukan hasil bagi dan sisa pembagian dari ( x 4 − x 3 + 7 x − 8 ) dibagi ( 1 − 5 x ) .

Tentukan hasil bagi dan sisa pembagian dari  dibagi .

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S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

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Pembahasan

Menggunakan metode horner dalam pembagian dua polinomial, diperoleh: Hasil bagi: Sisa pembagian: Atau dengan metode bersusun, diperoleh: Hasil bagi: Sisa pembagian:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 1 minus 5 x end cell equals 0 row cell 5 x end cell equals 1 row x equals cell 1 fifth end cell end table end style 

Menggunakan metode horner dalam pembagian dua polinomial, diperoleh:

begin mathsize 14px style long division with stack on the left by table row 1 cell negative 1 end cell 0 7 cell negative 8 end cell row space cell 1 fifth end cell cell negative 4 over 25 end cell cell 4 over 125 end cell cell 871 over 625 end cell end table yields table row 1 cell negative 4 over 5 end cell cell space space minus 4 over 25 end cell cell 871 over 125 end cell cell negative 4129 over 625 end cell end table pile 1 fifth end pile end long division end style 

Hasil bagi:

 begin mathsize 14px style negative 1 fifth open parentheses x cubed minus 4 over 5 x squared minus 4 over 25 x plus 871 over 125 close parentheses equals negative 1 fifth x cubed plus 4 over 25 x squared plus 4 over 125 x minus 871 over 625 end style   

Sisa pembagian: 

begin mathsize 14px style negative 4129 over 625 end style 

Atau dengan metode bersusun, diperoleh:

begin mathsize 14px style long division by 1 minus 5 x yields table row cell negative 1 fifth x cubed end cell cell plus 4 over 25 x squared end cell cell plus 4 over 125 x end cell cell negative 871 over 625 end cell end table pile table row cell x to the power of 4 end cell cell negative x cubed end cell cell plus 0 x squared end cell cell plus 7 x end cell cell negative 8 end cell end table stack attributes charalign center stackalign right end attributes stack attributes charalign center stackalign right end attributes table row cell x to the power of 4 end cell cell negative 1 fifth x cubed space space space space space space space space end cell cell space space end cell cell table row cell space space end cell cell space space space end cell end table end cell end table end stack horizontal line stack attributes charalign center stackalign right end attributes table row cell space space space space space minus 4 over 5 x cubed end cell cell plus 0 x squared space space space end cell space space space row cell space space space space space space minus 4 over 5 x cubed end cell cell plus 4 over 25 x squared end cell space space space end table horizontal line stack attributes charalign center stackalign right end attributes table row space space cell space space space space space space space space space space space space space space space minus 4 over 25 x squared end cell cell plus 7 x space space space space space end cell space row space space cell space space space space space space space space space space space space space minus 4 over 125 x squared end cell cell plus 4 over 125 x end cell space end table horizontal line stack attributes charalign center stackalign right end attributes table row space space space cell 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 871 over 125 x end cell cell negative 8 end cell row space space space cell 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 871 over 125 x end cell cell negative 871 over 625 end cell end table horizontal line table row space space space space cell 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 minus 4129 over 625 end cell end table end stack end stack end stack end stack end pile end long division end style 

Hasil bagi: 

begin mathsize 14px style negative 1 fifth x cubed plus 4 over 25 x squared plus 4 over 125 x minus 871 over 625 end style 

Sisa pembagian:

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