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Diketahui suku banyak P ( x ) = 2 x 4 + a x 3 − 3 x 2 + 5 x + b dibagi ( 1 − x 2 ) memberikan sisa ( 6 x − 5 ) . Nilai dari ab = ....

Diketahui suku banyak  dibagi  memberikan sisa . Nilai dari  

  1. begin mathsize 14px style negative 6 end style 

  2. begin mathsize 14px style negative 3 end style 

  3. begin mathsize 14px style 1 end style 

  4. begin mathsize 14px style 3 end style 

  5. begin mathsize 14px style 6 end style 

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

jawaban yang benar adalah E.

Pembahasan

Diketahui suku banyak dibagi memberikan sisa , maka: - Substitusi nilai ke - Substitusi nilai ke - Eliminanasi (1) dan (2) - Substitusi nilai ke (1) Sehingga: Jadi, jawaban yang benar adalah E.

Diketahui suku banyak begin mathsize 14px style straight P open parentheses straight x close parentheses equals 2 straight x to the power of 4 plus ax cubed minus 3 straight x squared plus 5 straight x plus straight b end style dibagi begin mathsize 14px style open parentheses 1 minus straight x squared close parentheses end style memberikan sisa begin mathsize 14px style open parentheses 6 straight x minus 5 close parentheses end style, maka:

begin mathsize 14px style space space space space space space space space open parentheses 1 minus straight x squared close parentheses equals 0 space space space space space space space open parentheses 1 squared minus straight x squared close parentheses equals 0 open parentheses 1 minus straight x close parentheses open parentheses 1 plus straight x close parentheses equals 0 straight x equals 1 space atau space straight x equals negative 1 end style 

- Substitusi nilai begin mathsize 14px style straight x equals 1 end style ke begin mathsize 14px style straight P open parentheses straight x close parentheses end style 

begin mathsize 14px style space space space space space straight P open parentheses straight x close parentheses equals 2 straight x to the power of 4 plus ax cubed minus 3 straight x squared plus 5 straight x plus straight b space space space space space straight P open parentheses 1 close parentheses equals 2 open parentheses 1 close parentheses to the power of 4 plus straight a open parentheses 1 close parentheses cubed minus 3 open parentheses 1 close parentheses squared plus 5 open parentheses 1 close parentheses plus straight b space space space 6 straight x plus 5 equals 2 open parentheses 1 close parentheses plus straight a open parentheses 1 close parentheses minus 3 open parentheses 1 close parentheses plus 5 plus straight b 6 open parentheses 1 close parentheses plus 5 equals 2 plus straight a minus 3 plus 5 plus straight b space space space space space 6 plus 5 equals 4 plus straight a plus straight b space space space space space space space space space 11 equals 4 plus straight a plus straight b space space space space space straight a plus straight b equals 7 space... space open parentheses 1 close parentheses end style  

- Substitusi nilai begin mathsize 14px style straight x equals negative 1 end style ke begin mathsize 14px style straight P open parentheses straight x close parentheses end style 

begin mathsize 14px style space space space space space space space space straight P left parenthesis straight x right parenthesis equals 2 straight x to the power of 4 plus ax cubed minus 3 straight x cubed plus 5 straight x plus straight b space space space space space straight P left parenthesis negative 1 right parenthesis equals 2 left parenthesis negative 1 right parenthesis to the power of 4 plus straight 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 straight b space space space space space space 6 straight x plus 5 equals 2 left parenthesis 1 right parenthesis plus straight a left parenthesis negative 1 right parenthesis minus 3 left parenthesis 1 right parenthesis minus 5 plus straight b 6 left parenthesis negative 1 right parenthesis plus 5 equals 2 minus straight a minus 3 minus 5 plus straight b space space space space space minus 6 plus 5 equals negative 6 minus straight a plus straight b space space space space space space space space space space minus 1 equals negative 6 minus straight a plus straight b space space space space space space space straight a minus straight b equals negative 5 space... space left parenthesis 2 right parenthesis end style 

- Eliminanasi (1) dan (2)

begin mathsize 14px style stack attributes charalign center stackalign right end attributes row straight a plus straight b equals 7 none end row row straight a minus straight b equals negative 5 end row horizontal line row 2 straight a equals 2 none end row row straight a equals 1 none end row end stack space plus end style 

- Substitusi nilai begin mathsize 14px style straight a end style ke (1)

begin mathsize 14px style straight a plus straight b equals 7 1 plus straight b equals 7 space space space space space space straight b equals 7 minus 1 space space space space space space straight b equals 6 end style 

Sehingga:

begin mathsize 14px style ab equals open parentheses 1 close parentheses open parentheses 6 close parentheses equals 6 end style 

Jadi, jawaban yang benar adalah E.

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