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Sisa pembagian dari polinomial   oleh  adalah ….

Pertanyaan

Sisa pembagian dari polinomial begin mathsize 14px style straight f open parentheses straight x close parentheses equals blank 2 straight x cubed minus 7 straight x squared minus 17 straight x plus 10 end style  oleh begin mathsize 14px style straight g open parentheses straight x close parentheses equals 2 straight x squared minus straight x minus 1 end style adalah ….

  1. -719

  2. - 7 x  + 19

  3. 197

  4. -197

  5. - 19 x  + 7

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Dari soal diberikan

begin mathsize 14px style straight f open parentheses straight x close parentheses equals blank 2 straight x cubed minus 7 straight x squared minus 17 straight x plus 10 end style

 Dibagi oleh begin mathsize 14px style straight g open parentheses straight x close parentheses equals 2 straight x squared minus straight x minus 1 end style    .

Perhatikan bahwa g(x) dapat difaktorkan menjadi

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight g open parentheses straight x close parentheses end cell equals cell 2 straight x squared minus straight x minus 1 end cell row blank equals cell open parentheses 2 straight x plus 1 close parentheses open parentheses straight x minus 1 close parentheses end cell end table end style 

Sehingga didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f open parentheses straight x close parentheses end cell equals cell straight g open parentheses straight x close parentheses times straight h open parentheses straight x close parentheses plus left parenthesis ax plus straight b right parenthesis end cell row cell 2 straight x cubed minus 7 straight x squared minus 17 straight x plus 10 end cell equals cell open parentheses 2 straight x squared minus straight x minus 1 close parentheses times straight h open parentheses straight x close parentheses plus ax plus straight b end cell row cell 2 straight x cubed minus 7 straight x squared minus 17 straight x plus 10 end cell equals cell open parentheses 2 straight x plus 1 close parentheses open parentheses straight x minus 1 close parentheses times straight h open parentheses straight x close parentheses plus ax plus straight b end cell row cell 2 straight x cubed minus 7 straight x squared minus 17 straight x plus 10 end cell equals cell 2 open parentheses straight x plus 1 half close parentheses open parentheses straight x minus 1 close parentheses times straight h open parentheses straight x close parentheses plus ax plus straight b end cell end table end style 

Dengan melakukan subtitusi begin mathsize 14px style straight x equals negative 1 half blank comma end style  didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 times open parentheses negative 1 half close parentheses cubed minus 7 times open parentheses negative 1 half close parentheses squared minus 17 times open parentheses negative 1 half close parentheses plus 10 end cell equals cell 2 open parentheses negative 1 half plus 1 half close parentheses open parentheses open parentheses negative 1 half close parentheses minus 1 close parentheses times straight h open parentheses negative 1 half close parentheses plus straight a times open parentheses negative 1 half close parentheses plus straight b end cell row cell negative 1 fourth minus 7 over 4 plus 17 over 2 plus 10 end cell equals cell 0 minus 1 half straight a plus straight b end cell row cell 33 over 2 end cell equals cell negative 1 half straight a plus straight b end cell row 33 equals cell negative straight a plus 2 straight b horizontal ellipsis left parenthesis straight i right parenthesis end cell end table end style 

Kemudian, dengan melakukan subtitusi = 1, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 times 1 cubed minus 7 times 1 squared minus 17 times 1 plus 10 end cell equals cell 2 open parentheses 1 plus 1 half close parentheses open parentheses 1 minus 1 close parentheses times straight h open parentheses 1 close parentheses plus straight a times 1 plus straight b end cell row cell 2 minus 7 minus 17 plus 10 end cell equals cell 0 plus straight a plus straight b end cell row cell negative 12 end cell equals cell straight a plus straight b horizontal ellipsis left parenthesis ii right parenthesis end cell end table end style 

Perhatikan bahwa, dari (ii) didapat

begin mathsize 14px style negative 12 equals straight a plus straight b minus 12 minus straight a equals straight b end style 

Sehingga dari (i) didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row 33 equals cell negative straight a plus 2 times left parenthesis negative 12 minus straight a right parenthesis end cell row 33 equals cell negative straight a minus 24 minus 2 straight a end cell row cell 33 plus 24 end cell equals cell negative 3 straight a end cell row 57 equals cell negative 3 straight a end cell row cell negative 19 end cell equals straight a end table end style 

Jadi, diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 12 minus straight a end cell equals straight b row cell negative 12 minus left parenthesis negative 19 right parenthesis end cell equals straight b row 7 equals straight b end table end style 

Jadi, sisa pembagian yang didapat adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight s open parentheses straight x close parentheses end cell equals cell ax plus straight b end cell row blank equals cell negative 19 straight x plus 7 end cell end table end style 

Dengan demikian, jawaban yang tepat adalah E.

32

5.0 (1 rating)

Marito Sofyola Gultom

Bantu banget

Pertanyaan serupa

Sisa pembagian dari polinomial  oleh g(x)=(x−3)(x+1) adalah ….

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