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Jika P ( x ) = a x 3 + b x 2 + ( a − 2 b ) x − a habis dibagi x 2 + 2 dan x + b , maka nilai ab adalah ....

Jika  habis dibagi  dan , maka nilai  adalah ....

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Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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Pembahasan

habis dibagi , maka adalah faktor habis dibagi dIperoleh Jadi, Jadi, jawaban yang tepat adalah D.

  • begin mathsize 14px style P open parentheses x close parentheses equals a x cubed plus b x squared plus open parentheses a minus 2 b close parentheses x minus a end style habis dibagi begin mathsize 14px style x squared plus 2 end style, maka begin mathsize 14px style x squared plus 2 end style adalah faktor

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a x cubed plus b x squared plus left parenthesis a minus 2 b right parenthesis x minus a end cell equals cell open parentheses x squared plus 2 close parentheses open parentheses a x minus a over 2 close parentheses end cell row cell a x cubed plus b x squared plus left parenthesis a minus 2 b right parenthesis x minus a end cell equals cell a x squared minus 1 half a x squared plus 2 a x minus a end cell row blank blank blank row cell a minus 2 b end cell equals cell 2 a end cell row cell negative 2 b end cell equals a row b equals cell negative 1 half a end cell row blank blank blank row cell space P left parenthesis x right parenthesis end cell equals cell a x cubed plus open parentheses negative 1 half a close parentheses x squared plus left parenthesis a minus 2 open parentheses negative 1 half a close parentheses right parenthesis x minus a end cell row blank equals cell a x cubed minus 1 half a x squared plus 2 a x minus a end cell end table end style 

 

  • begin mathsize 14px style P open parentheses x close parentheses equals a x cubed plus b x squared plus open parentheses a minus 2 b close parentheses x minus a end stylehabis dibagi begin mathsize 14px style x plus b end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus b end cell rightwards arrow cell x equals negative b end cell row blank equals cell negative open parentheses negative 1 half a close parentheses end cell row blank equals cell 1 half a end cell row cell P left parenthesis 1 half a right parenthesis end cell equals cell a open parentheses 1 half a close parentheses cubed plus b open parentheses 1 half a close parentheses squared plus left parenthesis a minus 2 b right parenthesis open parentheses 1 half a close parentheses minus a end cell row cell 1 over 8 a to the power of 4 minus 1 half a cubed plus a squared minus a end cell equals 0 row cell a to the power of 4 minus 4 a cubed plus 8 a squared minus 8 a end cell equals 0 row blank blank blank end table end style 

dIperoleh begin mathsize 14px style a equals 2 rightwards double arrow b equals negative 1 half a equals negative 1 end style

Jadi, begin mathsize 14px style a times b equals negative 2 end style 

Jadi, jawaban yang tepat adalah D.
 

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