Polinomial dibagi menghasilkan sisa . Jika dibagi , menghasilkan sisa . Jika dibagi , tentukan sisa baginya.

Pertanyaan

Polinomial $begin mathsize 14px style f left parenthesis x right parenthesis end style$ dibagi $begin mathsize 14px style left parenthesis x squared minus 4 right parenthesis end style$ menghasilkan sisa $begin mathsize 14px style left parenthesis 2 x minus 7 right parenthesis end style$ . Jika $undefined$ dibagi $begin mathsize 14px style left parenthesis x squared minus 9 right parenthesis end style$ , menghasilkan sisa $begin mathsize 14px style left parenthesis 5 x minus 11 right parenthesis end style$ . Jika $undefined$ dibagi $begin mathsize 14px style left parenthesis x squared minus x minus 6 right parenthesis end style$ , tentukan sisa baginya.

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Pembahasan Video:

Pembahasan Soal:

Ingat:

$begin mathsize 14px style f left parenthesis x right parenthesis equals p left parenthesis x right parenthesis times h left parenthesis x right parenthesis plus S left parenthesis x right parenthesis f left parenthesis x right parenthesis equals left parenthesis x minus a right parenthesis times h left parenthesis x right parenthesis plus S left parenthesis x right parenthesis f left parenthesis a right parenthesis equals S left parenthesis a right parenthesis end style$

$begin mathsize 14px style f left parenthesis x right parenthesis space dibagi space left parenthesis x squared minus 4 right parenthesis space bersisa space left parenthesis 2 x minus 7 right parenthesis end style$

$begin mathsize 14px style f left parenthesis x right parenthesis equals left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis times h subscript 1 left parenthesis x right parenthesis plus left parenthesis 2 x minus 7 right parenthesis f left parenthesis negative 2 right parenthesis equals 2 times open parentheses negative 2 close parentheses minus 7 rightwards arrow f left parenthesis negative 2 right parenthesis equals negative 11 f left parenthesis 2 right parenthesis equals 2 times 2 minus 7 rightwards arrow f left parenthesis 2 right parenthesis equals negative 4 end style$

$begin mathsize 14px style f left parenthesis x right parenthesis space dibagi space left parenthesis x squared minus 9 right parenthesis space bersisa space left parenthesis 5 x minus 11 right parenthesis end style$

$begin mathsize 14px style f left parenthesis x right parenthesis equals left parenthesis x plus 3 right parenthesis left parenthesis x minus 3 right parenthesis times h subscript 2 left parenthesis x right parenthesis plus left parenthesis 5 x minus 11 right parenthesis f left parenthesis negative 3 right parenthesis equals 5 times left parenthesis negative 3 right parenthesis minus 11 rightwards arrow f left parenthesis negative 3 right parenthesis equals negative 26 f left parenthesis 3 right parenthesis equals 5 times left parenthesis 3 right parenthesis minus 11 rightwards arrow f left parenthesis 3 right parenthesis equals 4 end style$

$begin mathsize 14px style f left parenthesis x right parenthesis space dibagi space left parenthesis x squared minus x minus 6 right parenthesis space bersisa space left parenthesis m x plus n right parenthesis end style$

$Error converting from MathML to accessible text.$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 m plus n end cell equals cell negative 11 end cell row cell negative 2 times 3 plus n end cell equals cell negative 11 end cell row cell negative 6 plus n end cell equals cell negative 11 end cell row n equals cell negative 5 end cell end table end style$

Didapat sisa $begin mathsize 14px style equals m x plus n equals 3 x minus 5 end style$

Jadi, $undefined$ dibagi $begin mathsize 14px style left parenthesis x squared minus x minus 6 right parenthesis end style$ bersisa $begin mathsize 14px style 3 x minus 5 end style$ .

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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