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Ditentukan begin mathsize 14px style g left parenthesis x right parenthesis equals x cubed plus p x squared plus q x plus 10 end style dan begin mathsize 14px style h left parenthesis x right parenthesis equals x squared minus 3 x plus 2 end style merupakan faktor dari g(x). Nilai p yang memenuhi adalah ....

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S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

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Pembahasan

begin mathsize 14px style g left parenthesis x right parenthesis equals x cubed plus p x squared plus q x plus 10 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell x squared minus 3 x plus 2 end cell row blank equals cell left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis end cell end table end style

h(x) faktor dari g(x) maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis 1 right parenthesis end cell equals 0 row cell left parenthesis 1 right parenthesis cubed plus p left parenthesis 1 right parenthesis squared plus q left parenthesis 1 right parenthesis plus 10 end cell equals 0 row cell p plus q end cell equals cell negative 11 space space space space space space space p e r s space 1 end cell row cell g left parenthesis 2 right parenthesis end cell equals 0 row cell left parenthesis 2 right parenthesis cubed plus p left parenthesis 2 right parenthesis squared plus q left parenthesis 2 right parenthesis plus 10 end cell equals 0 row cell 2 p plus q end cell equals cell negative 9 space space space space space space space space space p e r s space 2 end cell end table end style

begin mathsize 14px style table row cell p plus q end cell equals cell negative 11 end cell blank row cell 2 p plus q end cell equals cell negative 9 end cell minus row cell negative p end cell equals cell negative 2 end cell blank row p equals 2 blank row blank blank blank blank row blank blank blank blank end table end style

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