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Pertanyaan

Diketahui suku banyak $begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 4 end style$ dan $size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px equals size 14px 3 size 14px x to the power of size 14px 2 size 14px plus size 14px 5 size 14px x size 14px minus size 14px 6$ . Tentukan hasil dari $size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px plus size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis$ !

Pembahasan Soal:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end cell equals cell left parenthesis 2 x minus 4 right parenthesis plus left parenthesis 3 x squared plus 5 x minus 6 right parenthesis end cell row cell f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end cell equals cell 3 x squared plus 5 x plus 2 x minus 6 minus 4 end cell row cell f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end cell equals cell 3 x squared plus 7 x minus 10 end cell end table end style$

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Terakhir diupdate 30 April 2021

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Pertanyaan yang serupa

Diketahui polinomial dan . Jika , nilai

Pembahasan Soal:

Diketahui polinomial $m left parenthesis x right parenthesis equals 2 x cubed minus 5 x squared minus 4$ dan $n left parenthesis x right parenthesis equals x to the power of 4 minus 3 x squared plus 6$ . Jika $p left parenthesis x right parenthesis equals m left parenthesis x right parenthesis plus n left parenthesis x right parenthesis$ , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis x right parenthesis end cell equals cell m left parenthesis x right parenthesis plus n left parenthesis x right parenthesis end cell row blank equals cell open parentheses 2 x cubed minus 5 x squared minus 4 close parentheses plus open parentheses x to the power of 4 minus 3 x squared plus 6 close parentheses end cell row blank equals cell 2 x cubed minus 5 x squared minus 4 plus x to the power of 4 minus 3 x squared plus 6 end cell row blank equals cell x to the power of 4 plus 2 x cubed minus 8 x squared plus 2 end cell row blank blank blank row cell p left parenthesis negative 2 right parenthesis end cell equals cell left parenthesis negative 2 right parenthesis to the power of 4 plus 2 left parenthesis negative 2 right parenthesis cubed minus 8 left parenthesis negative 2 right parenthesis squared plus 2 equals 16 minus 16 minus 32 plus 2 end cell row blank equals cell negative 30 end cell end table$

Jadi, jawaban yang tepat adalah E

Roboguru

Sederhanakan:

Pembahasan Soal:

Untuk menyederhakan bentuk tersebut uraikan gunakan konsep perkalian, penjumlahan, dan pengurangan pada suku banyak sehingga:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x minus 1 close parentheses squared open parentheses x plus 2 close parentheses end cell equals cell left parenthesis x minus 1 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x plus 2 right parenthesis end cell row blank equals cell left parenthesis x squared minus 2 x plus 1 right parenthesis left parenthesis x plus 2 right parenthesis end cell row blank equals cell x cubed plus 2 x squared minus 2 x squared minus 4 x plus x plus 2 end cell row blank equals cell x cubed minus 3 x plus 2 end cell row cell left parenthesis x minus 1 right parenthesis squared left parenthesis x plus 2 right parenthesis minus open parentheses x plus 3 close parentheses end cell equals cell x cubed minus 3 x plus 2 minus open parentheses x plus 3 close parentheses end cell row blank equals cell x cubed minus 3 x plus 2 minus x minus 3 end cell row blank equals cell x cubed minus 3 x minus x plus 2 minus 3 end cell row blank equals cell x cubed minus 4 x minus 1 end cell end table end style$

Dengan demikian bentuk sederhana dari $begin mathsize 14px style open parentheses x minus 1 close parentheses squared open parentheses x plus 2 close parentheses minus open parentheses x plus 3 close parentheses end style$ adalah $begin mathsize 14px style x cubed minus 4 x minus 1 end style$ .

Roboguru

No Operasi Polinomial Hasil Operasi Keterangan 5

Pembahasan Soal:

Misal $begin mathsize 14px style f left parenthesis x right parenthesis equals a subscript 0 x to the power of n plus a subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus a subscript n end style$ , $begin mathsize 14px style g left parenthesis x right parenthesis equals b subscript 0 x to the power of n plus b subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus b subscript n end style$ dan $begin mathsize 14px style h left parenthesis x right parenthesis equals c subscript 0 x to the power of n plus c subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus c subscript n end style$ .

Perhatikan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets f open parentheses x close parentheses plus g open parentheses x close parentheses close square brackets plus h open parentheses x close parentheses end cell equals cell open square brackets open parentheses a subscript 0 x to the power of n plus a subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus a subscript n close parentheses plus open parentheses b subscript 0 x to the power of n plus b subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus b subscript n close parentheses close square brackets plus open parentheses c subscript 0 x to the power of n plus c subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus c subscript n close parentheses end cell row cell left square bracket f open parentheses x close parentheses plus g open parentheses x close parentheses right square bracket plus h left parenthesis x right parenthesis end cell equals cell open square brackets open parentheses a subscript 0 plus b subscript 0 close parentheses x to the power of n plus open parentheses a subscript 1 plus b subscript 1 close parentheses x to the power of n minus 1 end exponent plus horizontal ellipsis plus open parentheses a subscript n plus b subscript n close parentheses close square brackets plus open parentheses c subscript 0 x to the power of n plus c subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus c subscript n close parentheses end cell row cell left square bracket f open parentheses x close parentheses plus g open parentheses x close parentheses right square bracket plus h left parenthesis x right parenthesis end cell equals cell open parentheses a subscript 0 plus b subscript 0 plus c subscript 0 close parentheses x to the power of n plus open parentheses a subscript 1 plus b subscript 1 plus c subscript 1 close parentheses x to the power of n minus 1 end exponent plus horizontal ellipsis plus open parentheses a subscript n plus b subscript n plus c subscript n close parentheses end cell end table end style$

sehingga, hasil operasi $begin mathsize 14px style open square brackets f open parentheses x close parentheses plus g open parentheses x close parentheses close square brackets plus h open parentheses x close parentheses end style$ adalah $Error converting from MathML to accessible text.$ .

Roboguru

No Operasi Polinomial Hasil Operasi Keterangan 6

Pembahasan Soal:

Misal $begin mathsize 14px style f left parenthesis x right parenthesis equals a subscript 0 x to the power of n plus a subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus a subscript n end style$ , $begin mathsize 14px style g left parenthesis x right parenthesis equals b subscript 0 x to the power of n plus b subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus b subscript n end style$ dan $begin mathsize 14px style g left parenthesis x right parenthesis equals c subscript 0 x to the power of n plus c subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus c subscript n end style$ .

Perhatikan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses plus open square brackets g open parentheses x close parentheses plus h open parentheses x close parentheses close square brackets end cell equals cell open parentheses a subscript 0 x to the power of n plus a subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus a subscript n close parentheses plus open square brackets open parentheses b subscript 0 x to the power of n plus b subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus b subscript n close parentheses plus open parentheses c subscript 0 x to the power of n plus c subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus c subscript n close parentheses close square brackets end cell row cell f open parentheses x close parentheses plus open square brackets g open parentheses x close parentheses plus h open parentheses x close parentheses close square brackets end cell equals cell a subscript 0 x to the power of n plus a subscript 1 x to the power of n minus 1 end exponent plus horizontal ellipsis plus a subscript n plus open parentheses b subscript 0 plus c subscript 0 close parentheses x to the power of n plus open parentheses b subscript 1 plus c subscript 1 close parentheses x to the power of n minus 1 end exponent plus horizontal ellipsis plus open parentheses b subscript n plus c subscript n close parentheses end cell row cell f open parentheses x close parentheses plus open square brackets g open parentheses x close parentheses plus h open parentheses x close parentheses close square brackets end cell equals cell open parentheses a subscript 0 plus b subscript 0 plus c subscript 0 close parentheses x to the power of n plus open parentheses a subscript 1 plus b subscript 1 plus c subscript 1 close parentheses x to the power of n minus 1 end exponent plus horizontal ellipsis plus open parentheses a subscript n plus b subscript n plus c subscript n close parentheses end cell row blank blank blank end table end style$

sehingga, hasil operasi $begin mathsize 14px style f open parentheses x close parentheses plus open square brackets g open parentheses x close parentheses plus h open parentheses x close parentheses close square brackets end style$ adalah $Error converting from MathML to accessible text.$ .

Roboguru

Diberikan polynomial Tentukan : a. serta derajatnya

Pembahasan Soal:

Kita kalikan dahulu lalu dijumlahkan kemudian kita lihat derajatnya. Derajat adalah pangkat tertinggi dari suku banyak.

$A open parentheses x close parentheses times B open parentheses x close parentheses plus C open parentheses x close parentheses equals open parentheses x squared minus 3 x plus 2 close parentheses open parentheses x cubed minus 2 close parentheses plus open parentheses x cubed minus 4 x squared plus 5 x close parentheses equals x to the power of 5 minus 2 x squared minus 3 x to the power of 4 plus 6 x plus 2 x cubed minus 4 plus x cubed minus 4 x squared plus 5 x equals x to the power of 5 minus 3 x to the power of 4 plus 3 x cubed minus 6 x squared plus 11 x minus 4$

Sehingga derajatnya adalah $5$ yang terdapat di $x to the power of 5$ .

Jadi, $A open parentheses x close parentheses times B open parentheses x close parentheses plus C open parentheses x close parentheses$ dan derajatnya adalah $x to the power of 5 minus 3 x to the power of 4 plus 3 x cubed minus 6 x squared plus 11 x minus 4$ dan $5$ .

Roboguru