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Pembagian suku banyak  dibagi dengan  memberikan sisa 7. Hitunglah nilai

Pertanyaan

Pembagian suku banyak begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x to the power of 4 plus 10 x cubed plus open parentheses p plus 1 close parentheses x plus 9 end style dibagi dengan begin mathsize 14px style open parentheses 3 x plus 1 close parentheses end style memberikan sisa 7. Hitunglah nilai begin mathsize 14px style p. end style 

Pembahasan Soal:

Perhatikan penghitungan berikut!

 begin mathsize 14px style long division by 3 x plus 1 yields table row cell x cubed plus 3 x squared minus x plus fraction numerator p plus 2 over denominator 3 end fraction end cell end table pile bottom enclose table row cell 3 x to the power of 4 plus 10 x cubed plus left parenthesis p plus 1 right parenthesis x plus 9 end cell row cell 3 x to the power of 4 plus x cubed space space space space space space space space minus end cell end table end enclose bottom enclose table row cell 9 x cubed plus left parenthesis p plus 1 right parenthesis x plus 9 end cell row cell 9 x cubed plus 3 x squared space space space space space space space space minus end cell end table end enclose bottom enclose table row cell negative 3 x squared plus left parenthesis p plus 1 right parenthesis x plus 9 end cell row cell negative 3 x squared minus x space space space space space space space space space minus end cell end table end enclose bottom enclose table row cell left parenthesis p plus 1 right parenthesis x plus x plus 9 end cell row cell left parenthesis p plus 2 right parenthesis x plus fraction numerator left parenthesis p plus 2 right parenthesis over denominator 3 end fraction space minus end cell end table end enclose table row cell 9 minus fraction numerator left parenthesis p plus 2 right parenthesis over denominator 3 end fraction end cell end table end pile end long division  sisanya space yaitu space 9 minus fraction numerator left parenthesis p plus 2 right parenthesis over denominator 3 end fraction space sehingga 9 minus fraction numerator left parenthesis p plus 2 right parenthesis over denominator 3 end fraction equals 7 fraction numerator 27 minus p minus 2 over denominator 3 end fraction equals 7 25 minus p equals 7 left parenthesis 3 right parenthesis 25 minus p equals 21 p equals 25 minus 21 p equals 4 end style 

Jadi, nilai begin mathsize 14px style p end style adalah 4.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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