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Sisa pembagian oleh x+3 adalah 2. Jika p(x) habis dibagi oleh x+1 dan x-1 , maka A+2B-3C=.....

Sisa pembagian p left parenthesis x right parenthesis equals x cubed plus A x squared plus B x plus C oleh x+3 adalah 2. Jika p(x) habis dibagi oleh x+1 dan x-1 , maka A+2B-3C=.....

  1. 10

  2. 11

  3. 12

  4. 13

  5. 14

Jawaban:

Karena space straight p left parenthesis straight x right parenthesis space dibagi space straight x plus 3 space bersisa space 2 comma space maka space box enclose straight p left parenthesis negative 3 right parenthesis equals 2 end enclose.  Sehingga  straight p left parenthesis straight x right parenthesis equals straight x cubed plus Ax squared plus Bx plus straight C  straight p left parenthesis negative 3 right parenthesis equals left parenthesis negative 3 right parenthesis cubed plus straight A left parenthesis negative 3 right parenthesis squared plus straight B left parenthesis negative 3 right parenthesis plus straight C  2 equals negative 27 plus 9 straight A minus 3 straight B plus straight C  box enclose 9 straight A minus 3 straight B plus straight C equals 29 end enclose... left parenthesis 1 right parenthesis    Karena space straight p left parenthesis straight x right parenthesis space habis space dibagi space straight x plus 1 comma space maka space box enclose straight p left parenthesis negative 1 right parenthesis equals 0 end enclose.  straight p left parenthesis straight x right parenthesis equals straight x cubed plus Ax squared plus Bx plus straight C  straight p left parenthesis negative 1 right parenthesis equals left parenthesis negative 1 right parenthesis cubed plus straight A left parenthesis negative 1 right parenthesis squared plus straight B left parenthesis negative 1 right parenthesis plus straight C  0 equals negative 1 plus straight A minus straight B plus straight C  box enclose straight A minus straight B plus straight C equals 1 end enclose... left parenthesis 2 right parenthesis    Karena space straight p left parenthesis straight x right parenthesis space habis space dibagi space straight x minus 1 comma space maka space box enclose straight p left parenthesis 1 right parenthesis equals 0 end enclose.  straight p left parenthesis straight x right parenthesis equals straight x cubed plus Ax squared plus Bx plus straight C  straight p left parenthesis 1 right parenthesis equals left parenthesis 1 right parenthesis cubed plus straight A left parenthesis 1 right parenthesis squared plus straight B left parenthesis 1 right parenthesis plus straight C  0 equals 1 plus straight A plus straight B plus straight C  box enclose straight A plus straight B plus straight C equals negative 1 end enclose... left parenthesis 3 right parenthesis    Eliminasi space persamaan space left parenthesis 2 right parenthesis space dan space left parenthesis 3 right parenthesis  straight A minus straight B plus straight C equals 1  bottom enclose straight A plus straight B plus straight C equals negative 1 minus end enclose  minus 2 straight B equals 2  box enclose straight B equals negative 1 end enclose    Eliminasi space persamaan space left parenthesis 1 right parenthesis space dan space left parenthesis 2 right parenthesis space didapat  bottom enclose 9 straight A minus 3 straight B plus straight C equals 29  space space space space straight A minus straight B plus straight C equals 1 minus end enclose  8 straight A minus 2 straight B equals 28  4 straight A minus straight B equals 14  4 straight A minus left parenthesis negative 1 right parenthesis equals 14  4 straight A equals 13  box enclose straight A equals 13 over 4 end enclose    Dari space persamaan space left parenthesis 3 right parenthesis  straight A plus straight B plus straight C equals negative 1  13 over 4 minus 1 plus straight C equals negative 1  box enclose straight C equals negative 13 over 4 end enclose    Maka  straight A plus 2 straight B minus 3 straight C equals 13 over 4 plus 2 left parenthesis negative 1 right parenthesis minus 3 open parentheses negative 13 over 4 close parentheses  equals 13 over 4 minus 2 plus 39 over 4  equals box enclose 11

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