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Diketahui suku banyak  habis dibagi . Jika  dibagi...

Diketahui suku banyak begin mathsize 14px style P open parentheses x close parentheses equals x to the power of 4 plus 2 x cubed minus 9 x squared minus 2 x plus k end style habis dibagi begin mathsize 14px style x minus 2 end style. Jika undefined dibagi begin mathsize 14px style x minus 1 end style sisanya adalah ....

  1. 8space    

  2. 4undefined   

  3. 0  

  4. - 3  

  5. - 2  

Jawaban:

suku banyak begin mathsize 14px style P open parentheses x close parentheses equals x to the power of 4 plus 2 x cubed minus 9 x squared minus 2 x plus k end style habis dibagi begin mathsize 14px style x minus 2 end style artinya begin mathsize 14px style straight p open parentheses 2 close parentheses equals 0 end style, sehingga :
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight p open parentheses straight x close parentheses end cell equals 0 row cell straight x to the power of 4 plus 2 straight x cubed minus 9 straight x squared minus 2 straight x plus straight k end cell equals 0 row cell straight p open parentheses 2 close parentheses end cell equals 0 row cell 2 to the power of 4 plus 2 open parentheses 2 close parentheses cubed minus 9 open parentheses 2 close parentheses squared minus 2 open parentheses 2 close parentheses plus straight k end cell equals 0 row cell 16 plus 16 minus 36 minus 4 plus straight k end cell equals 0 row cell negative 8 plus straight k end cell equals 0 row straight k equals 8 end table end style 
 

Selanjutnya mencari sisa Jika undefined dibagi begin mathsize 14px style x minus 1 end style
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight x minus 1 end cell equals 0 row straight x equals 1 row maka colon blank row cell straight p open parentheses straight x close parentheses end cell equals cell straight x to the power of 4 plus 2 straight x cubed minus 9 straight x squared minus 2 straight x plus 8 end cell row cell straight p open parentheses 1 close parentheses end cell equals cell 1 to the power of 4 plus 2 open parentheses 1 close parentheses cubed minus 9 open parentheses 1 close parentheses squared minus 2 open parentheses 1 close parentheses plus 8 end cell row blank equals cell 1 plus 2 minus 9 minus 2 plus 8 end cell row blank equals 0 row sisa equals 0 end table end style 
 

Jadi, undefined dibagi begin mathsize 14px style x minus 1 end style sisanya adalah 0

Jadi, jawaban yang tepat adalah C 

0

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