Roboguru

Diketahui suku banyak  dan . Tentukan hasil dari !

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 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 30 April 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

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

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved