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Diketahui . Jika hasil penjumlahan antara dengan adalah  . Maka bentuk polinomial  adalah...

Pertanyaan

Diketahui P left parenthesis x right parenthesis equals 4 x cubed plus 2 x squared plus x minus 5. Jika hasil penjumlahan antaraspace P left parenthesis x right parenthesis dengan G left parenthesis x right parenthesis adalah 4 x cubed plus 3 x squared plus 2 x plus 1 . Maka bentuk polinomial G left parenthesis x right parenthesis adalah...

Pembahasan Video:

Pembahasan Soal:

P(x)+G(x)4x3+2x2+x5+G(x)G(x)G(x)G(x)G(x)======4x3+3x2+2x+14x3+3x2+2x+14x3+3x2+2x+1(4x3+2x2+x5)4x3+3x2+2x+14x32x2x+53x22x2+2xx+1+5x2+x+6

Jadi, bentuk polinomial G left parenthesis x right parenthesis adalah Error converting from MathML to accessible text..

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 17 September 2021

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Pertanyaan yang serupa

Diketahui polinomial  dan . Jika , tentukan: a. polinomial ;

Pembahasan Soal:

Diketahui: begin mathsize 14px style h open parentheses x close parentheses equals 2 f squared open parentheses x close parentheses minus f open parentheses x close parentheses cross times g open parentheses x close parentheses end style 

Oleh karena itu, undefined dapat kita tuliskan sebagai berikut.

  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 2 f squared left parenthesis x right parenthesis minus f left parenthesis x right parenthesis cross times g left parenthesis x right parenthesis end cell row blank equals cell 2 left parenthesis x squared minus 4 x plus 2 right parenthesis squared minus left parenthesis x squared minus 4 x plus 2 right parenthesis cross times left parenthesis x cubed minus 3 x squared minus 2 x plus 1 right parenthesis end cell row blank equals cell 2 left parenthesis x squared minus 4 x plus 2 right parenthesis cross times left parenthesis x squared minus 4 x plus 2 right parenthesis minus left parenthesis x squared minus 4 x plus 2 right parenthesis cross times left parenthesis x cubed minus 3 x squared minus 2 x plus 1 right parenthesis end cell row blank equals cell 2 left parenthesis x to the power of 4 minus 4 x cubed plus 2 x squared minus 4 x cubed plus 16 x squared minus 8 x plus 2 x squared minus 8 x plus 4 right parenthesis minus left parenthesis x to the power of 5 minus 3 x to the power of 4 minus 2 x cubed plus x squared minus 4 x to the power of 4 plus 12 x cubed plus 8 x squared minus 4 x plus 2 x cubed minus 6 x squared minus 4 x plus 2 right parenthesis end cell row blank equals cell 2 open parentheses x to the power of 4 minus 4 x cubed minus 4 x cubed plus 2 x squared plus 16 x squared plus 2 x squared minus 8 x minus 8 x plus 4 close parentheses minus left parenthesis x to the power of 5 minus 3 x to the power of 4 minus 4 x to the power of 4 minus 2 x cubed plus 12 x cubed plus 2 x cubed plus x squared plus 8 x squared minus 6 x squared minus 4 x minus 4 x plus 2 right parenthesis end cell row blank equals cell 2 left parenthesis x to the power of 4 minus 8 x cubed plus 20 x squared minus 16 x plus 4 right parenthesis minus left parenthesis x to the power of 5 minus 7 x to the power of 4 plus 12 x cubed plus 3 x squared minus 8 x plus 2 right parenthesis end cell row blank equals cell 2 x to the power of 4 minus 16 x cubed plus 40 x squared minus 32 x plus 8 minus x to the power of 5 plus 7 x to the power of 4 minus 12 x cubed minus 3 x squared plus 8 x minus 2 end cell row blank equals cell negative x to the power of 5 plus 2 x to the power of 4 plus 7 x to the power of 4 minus 16 x cubed minus 12 x cubed plus 40 x squared minus 3 x squared minus 32 x plus 8 x plus 8 minus 2 end cell row blank equals cell negative x to the power of 5 plus 9 x to the power of 4 minus 28 x cubed plus 37 x squared minus 24 x plus 6 end cell end table end style 

Jadi, polinomial undefined adalah  undefined.

0

Roboguru

Diberikan polynomial Tentukan : b. serta derajatnya

Pembahasan Soal:

Dalam operasi hitung dua fungsi kita dapat melakukan operasi dengan variabel yang memiliki pangkat yang sama. Selain itu, derajat polinomal adalah pangkat tertinggi dari suku-suku yang ada pada polinomial tersebut.

Kita kerjakan dahulu operasi hitung polinomialnya kemudian kita lihat derajatnya. Derajat adalah pangkat tertinggi dari suku banyak.

begin mathsize 11px style open square brackets C open parentheses x close parentheses minus B open parentheses x close parentheses close square brackets open square brackets A open parentheses x close parentheses plus C open parentheses x close parentheses close square brackets equals open square brackets open parentheses x cubed minus 4 x squared plus 5 x close parentheses minus open parentheses x cubed minus 2 close parentheses close square brackets open square brackets open parentheses x squared minus 3 x plus 2 close parentheses plus open parentheses x cubed minus 4 x squared plus 5 x close parentheses close square brackets equals open square brackets negative 4 x squared plus 5 x plus 2 close square brackets open square brackets x cubed minus 3 x squared plus 2 x plus 2 close square brackets equals negative 4 x to the power of 5 plus 17 x to the power of 4 minus 21 x cubed minus 4 x squared plus 14 x plus 4 end style

Sehingga derajatnya adalah 5 yang terdapat di negative 4 x to the power of 5.

Jadi, hasil operasi hitung polinomial open square brackets C open parentheses x close parentheses minus B open parentheses x close parentheses close square brackets open square brackets A open parentheses x close parentheses plus C open parentheses x close parentheses close square brackets adalah negative 4 x to the power of 5 plus 17 x to the power of 4 minus 21 x cubed minus 4 x squared plus 14 x plus 4 yang berderajat 5.

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Roboguru

Diketahui polinomial  dan . Jika , tentukan: c. koefisien  dari polinomial .

Pembahasan Soal:

Diketahui polinomial begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus 4 x plus 2 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x cubed minus 3 x squared minus 2 x plus 1 end style.

Fungsi begin mathsize 14px style h open parentheses x close parentheses equals 2 f squared open parentheses x close parentheses minus f open parentheses x close parentheses cross times g open parentheses x close parentheses end style.

Bentuk kuadrat fungsi f squared left parenthesis x right parenthesis dapat dihitung seperti berikut :

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 times f squared left parenthesis x right parenthesis end cell row blank equals cell 2 times f left parenthesis x right parenthesis times f left parenthesis x right parenthesis end cell row blank equals cell 2 times open parentheses x squared minus 4 x plus 2 close parentheses open parentheses x squared minus 4 x plus 2 close parentheses end cell row blank equals cell 2 times left parenthesis x to the power of 4 minus 4 x cubed plus 2 x squared minus 4 x cubed plus 16 x squared minus 8 x end cell row blank blank cell plus 2 x squared minus 8 x plus 4 right parenthesis end cell row blank equals cell 2 times open parentheses x to the power of 4 minus 8 x cubed plus 20 x squared minus 16 x plus 4 close parentheses end cell row blank equals cell 2 x to the power of 4 minus 16 x cubed plus 40 x squared minus 32 x plus 8 end cell end table  

Bentuk perkalian fungsi f left parenthesis x right parenthesis space dan space g left parenthesis x right parenthesis adalah :

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f left parenthesis x right parenthesis times g left parenthesis x right parenthesis end cell row blank equals cell open parentheses x squared minus 4 x plus 2 close parentheses open parentheses x cubed minus 3 x squared minus 2 x plus 1 close parentheses end cell row blank equals cell x to the power of 5 minus 3 x to the power of 4 minus 2 x cubed plus x squared minus 4 x to the power of 4 plus 12 x cubed plus 8 x squared end cell row blank blank cell negative 4 x plus 2 x cubed minus 6 x squared minus 4 x plus 2 end cell row blank equals cell x to the power of 5 minus 7 x to the power of 4 plus 12 x cubed plus 3 x squared minus 8 x plus 2 end cell end table 

Oleh karena itu, begin mathsize 14px style h left parenthesis x right parenthesis end style dapat kita tuliskan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell 2 times f squared left parenthesis x right parenthesis minus f left parenthesis x right parenthesis times g left parenthesis x right parenthesis end cell row blank equals cell open parentheses 2 x to the power of 4 minus 16 x cubed plus 40 x squared minus 32 x plus 8 close parentheses end cell row blank blank cell negative open parentheses x to the power of 5 minus 7 x to the power of 4 plus 12 x cubed plus 3 x squared minus 8 x plus 2 close parentheses end cell row blank equals cell 2 x to the power of 4 minus 16 x cubed plus 40 x squared minus 32 x plus 8 end cell row blank blank cell negative x to the power of 5 plus 7 x to the power of 4 minus 12 x cubed minus 3 x squared plus 8 x minus 2 end cell row blank equals cell negative x to the power of 5 plus 9 x to the power of 4 minus 28 x cubed plus 37 x squared minus 24 x plus 6 end cell end table    

Dari hasil diatas bisa dilihat bahwa koefisien begin mathsize 14px style x cubed end style dari polinomial undefined adalah begin mathsize 14px style negative 28 end style.

0

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.

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Roboguru

Diketahui polinomial  dan . Jika , tentukan: b. derajat polinomial ; dan

Pembahasan Soal:

Diketahui: begin mathsize 14px style h open parentheses x close parentheses equals 2 f squared open parentheses x close parentheses minus f open parentheses x close parentheses cross times g open parentheses x close parentheses end style 

Oleh karena itu, begin mathsize 14px style h left parenthesis x right parenthesis end style dapat kita tuliskan sebagai berikut.

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 2 f squared left parenthesis x right parenthesis minus f left parenthesis x right parenthesis cross times g left parenthesis x right parenthesis end cell row blank equals cell 2 left parenthesis x squared minus 4 x plus 2 right parenthesis squared minus left parenthesis x squared minus 4 x plus 2 right parenthesis cross times left parenthesis x cubed minus 3 x squared minus 2 x plus 1 right parenthesis end cell row blank equals cell 2 left parenthesis x squared minus 4 x plus 2 right parenthesis times left parenthesis x squared minus 4 x plus 2 right parenthesis minus left parenthesis x squared minus 4 x plus 2 right parenthesis times left parenthesis x cubed minus 3 x squared minus 2 x plus 1 right parenthesis end cell row blank equals cell 2 left parenthesis x to the power of 4 minus 4 x cubed plus 2 x squared minus 4 x cubed plus 16 x squared minus 8 x plus 2 x squared minus 8 x plus 4 right parenthesis minus left parenthesis x to the power of 5 minus 3 x to the power of 4 minus 2 x cubed plus x squared minus 4 x to the power of 4 plus 12 x cubed plus 8 x squared minus 4 x plus 2 x cubed minus 6 x squared minus 4 x plus 2 right parenthesis end cell row blank equals cell 2 left parenthesis x to the power of 4 minus 4 x cubed minus 4 x cubed plus 2 x squared plus 16 x squared plus 2 x squared minus 8 x minus 8 x plus 4 right parenthesis minus left parenthesis x to the power of 5 minus 3 x to the power of 4 minus 4 x to the power of 4 minus 2 x cubed plus 12 x cubed plus 2 x cubed plus x squared plus 8 x squared minus 6 x squared minus 4 x minus 4 x plus 2 right parenthesis end cell row blank equals cell 2 left parenthesis x to the power of 4 minus 8 x cubed plus 20 x squared minus 16 x plus 4 right parenthesis minus left parenthesis x to the power of 5 minus 7 x to the power of 4 plus 12 x cubed plus 3 x squared minus 8 x plus 2 right parenthesis end cell row blank equals cell 2 x to the power of 4 minus 16 x cubed plus 40 x squared minus 32 x plus 8 minus x to the power of 5 plus 7 x to the power of 4 minus 12 x cubed minus 3 x squared plus 8 x minus 2 end cell row blank equals cell negative x to the power of 5 plus 2 x to the power of 4 plus 7 x to the power of 4 minus 16 x cubed minus 12 x cubed plus 40 x squared minus 3 x squared minus 32 x plus 8 x plus 8 minus 2 end cell row blank equals cell negative x to the power of 5 plus 9 x to the power of 4 minus 28 x cubed plus 37 x squared minus 24 x plus 6 end cell end table end style

Ingat bahwa derajat adalah pangkat tertinggi dalam suatu suku banyak.

Dari hasil diatas bisa dilihat bahwa derajat polinomial undefined adalah 5.

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Roboguru

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