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Pertanyaan

Diketahui begin mathsize 14px style h left parenthesis x right parenthesis equals x squared plus 3 x minus 4 end style merupakan salah satu faktor begin mathsize 14px style g left parenthesis x right parenthesis equals x to the power of 4 plus 2 x cubed minus a x squared minus 14 x plus b end style. Jika undefined dibagi oleh undefined, menghasilkan sisa ....

  1. begin mathsize 14px style 0 end style 

  2. undefined 

  3. begin mathsize 14px style 9 end style 

  4. begin mathsize 14px style 12 end style 

  5. undefined 

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

Jawaban yang tepat adalah E.

Pembahasan

Ingat: Jika begin mathsize 14px style open parentheses x minus k close parentheses end style merupakan faktor dari polinomial undefined maka begin mathsize 14px style p left parenthesis k right parenthesis equals 0 end style 

  • begin mathsize 14px style g left parenthesis x right parenthesis equals x to the power of 4 plus 2 x cubed minus a x squared minus 14 x plus b end style 
  • begin mathsize 14px style h left parenthesis x right parenthesis equals x squared plus 3 x minus 4 end style 
    begin mathsize 14px style x squared plus 3 x minus 4 equals open parentheses x plus 4 close parentheses open parentheses x minus 1 close parentheses end style 

 Jika undefined merupakan faktor dari begin mathsize 14px style g left parenthesis x right parenthesis end style 
Maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell x to the power of 4 plus 2 x cubed minus a x squared minus 14 x plus b end cell row cell bullet f left parenthesis negative 4 right parenthesis end cell equals 0 row cell left parenthesis negative 4 right parenthesis to the power of 4 plus 2 times left parenthesis negative 4 right parenthesis cubed minus a times open parentheses negative 4 close parentheses squared minus 14 times left parenthesis negative 4 right parenthesis plus b end cell equals 0 row cell 256 minus 128 minus 16 a plus 56 plus b end cell equals 0 row cell negative 16 a plus b end cell equals cell negative 184 space horizontal ellipsis space pers space left parenthesis 1 right parenthesis end cell row blank blank blank row cell bullet f left parenthesis 1 right parenthesis end cell equals 0 row cell 1 blank to the power of 4 plus 2 times 1 blank cubed minus a times 1 blank squared minus 14 times 1 plus b end cell equals 0 row cell negative a plus b end cell equals cell 11 space horizontal ellipsis space pers space left parenthesis 2 right parenthesis end cell end table end style  

Gunakan eliminasi dan substitusi untuk menentukan nilai begin mathsize 14px style a space end style dan begin mathsize 14px style b end style 
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 16 a plus b end cell equals cell negative 184 end cell row blank blank cell space space space space bottom enclose negative a plus b equals 11 space space space space space space end enclose space minus end cell row cell space space space space minus 15 a space end cell equals cell negative 195 end cell row cell space space space space space space space space space space space space space a end cell equals cell space 13 end cell row blank blank blank row cell negative a plus b end cell equals 11 row b equals cell 11 plus a end cell row b equals cell 11 plus 13 end cell row blank equals 24 end table end style 

Sehingga sisa pembagian undefined oleh begin mathsize 14px style open parentheses x plus 1 close parentheses end style adalah begin mathsize 14px style g left parenthesis negative 1 right parenthesis end style   

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell x to the power of 4 plus 2 x cubed minus 13 x squared minus 14 x plus 24 end cell row cell g left parenthesis negative 1 right parenthesis end cell equals cell left parenthesis negative 1 right parenthesis to the power of 4 plus 2 times left parenthesis negative 1 right parenthesis cubed minus 13 times left parenthesis negative 1 right parenthesis squared minus 14 times left parenthesis negative 1 right parenthesis plus 24 end cell row blank equals cell 1 minus 2 minus 13 plus 14 plus 24 end cell row blank equals 24 end table end style 

Jadi, Jawaban yang tepat adalah E.

54

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