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Tentukan hasil operasi polinomial berikut, kemudian sebutkan derajat, koefisien masing-masing dan suku tetap dari polinomial tersebut. b. ((3x2+x−6)(2x−1))−((5−2x)(x2−3))

Pertanyaan

Tentukan hasil operasi polinomial berikut, kemudian sebutkan derajat, koefisien masing-masing dan suku tetap dari polinomial tersebut.

b. begin mathsize 14px style open parentheses open parentheses 3 x squared plus x minus 6 close parentheses open parentheses 2 x minus 1 close parentheses close parentheses minus open parentheses open parentheses 5 minus 2 x close parentheses open parentheses x squared minus 3 close parentheses close parentheses end style

Pembahasan Soal:

Hasil operasi dimulai dengan perkalian, kemudian koefisien yang memiliki variabel dan derajat yang sama bisa dioperasikan.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis open parentheses 3 x squared plus x minus 6 close parentheses open parentheses 2 x minus 1 close parentheses right parenthesis minus open parentheses open parentheses 5 minus 2 x close parentheses open parentheses x squared minus 3 close parentheses close parentheses end cell equals cell 3 x squared left parenthesis 2 x minus 1 right parenthesis plus x left parenthesis 2 x minus 1 right parenthesis minus 6 left parenthesis 2 x minus 1 right parenthesis minus 5 left parenthesis x squared minus 3 right parenthesis minus left parenthesis negative 2 x right parenthesis left parenthesis x squared minus 3 right parenthesis end cell row blank equals cell 3 x squared left parenthesis 2 x right parenthesis plus 3 x squared left parenthesis negative 1 right parenthesis plus x left parenthesis 2 x right parenthesis plus x left parenthesis negative 1 right parenthesis minus 6 left parenthesis 2 x right parenthesis minus 6 left parenthesis negative 1 right parenthesis minus 5 left parenthesis x squared right parenthesis minus 5 left parenthesis negative 3 right parenthesis plus 2 x left parenthesis x squared right parenthesis plus 2 x left parenthesis negative 3 right parenthesis end cell row blank equals cell 6 x cubed minus 3 x squared plus 2 x squared minus x minus 12 x plus 6 minus 5 x squared plus 15 plus 2 x cubed minus 6 x space space end cell row blank equals cell 6 x cubed plus 2 x cubed minus 3 x squared plus 2 x squared minus 5 x squared minus x minus 12 x minus 6 x plus 6 plus 15 space space end cell row blank equals cell 8 x cubed minus 6 x squared minus 19 x plus 21 end cell end table end style

Pangkat tertinggi yaitu 3, maka polinom ini berderajat 3. Koefisien suku berderajat 3 (Error converting from MathML to accessible text.) yaitu 8. Koefisien suku berderajat 2 (Error converting from MathML to accessible text.) yaitu begin mathsize 14px style negative 6 end style. Koefisien suku berderajat 1 (begin mathsize 14px style x end style) yaitu begin mathsize 14px style negative 19 end style. Suku tetap yaitu 21.

Jadi, hasil operasi yaitu Error converting from MathML to accessible text., berderajat 3, koefisien Error converting from MathML to accessible text. yaitu  8, koefisien Error converting from MathML to accessible text. yaitu begin mathsize 14px style negative 6 end style, koefisien begin mathsize 14px style x end style yaitu begin mathsize 14px style negative 19 end style, dan suku tetap yaitu 21.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Hermawan

Mahasiswa/Alumni Universitas Lampung

Terakhir diupdate 05 Oktober 2021

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Pertanyaan yang serupa

Diketahui polinomial p, q, dan r dengan p(−5)=−8, q(−5)=−2, r(−5)=3. Nilai polinomial f(x)=p(x)−q(x)×r(x) untuk x=−5 adalah ....

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell p left parenthesis x right parenthesis minus q left parenthesis x right parenthesis cross times r left parenthesis x right parenthesis end cell row cell f left parenthesis negative 5 right parenthesis end cell equals cell p left parenthesis negative 5 right parenthesis minus q left parenthesis negative 5 right parenthesis cross times r left parenthesis negative 5 right parenthesis end cell row blank equals cell negative 8 minus left parenthesis negative 2 right parenthesis cross times 3 end cell row blank equals cell negative 2 end cell end table end style

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Roboguru

Diketahui polinomial f(x)=x2−4x+2 dan g(x)=x3−3x2−2x+1. Jika h(x)=2f2(x)−f(x)×g(x), tentukan: b. derajat polinomial h(x); 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

Diketahui polinomial f(x)=x2−3 dan g(x)=x3−4x2−5x+2. Jika h(x)=3f(x)−f(x)⋅g(x), tentukan polinomial h(x).

Pembahasan Soal:

Polinomial begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus 3 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x cubed minus 4 x squared minus 5 x plus 2 end style

Akan ditentukan begin mathsize 14px style h left parenthesis x right parenthesis equals 3 f left parenthesis x right parenthesis minus f left parenthesis x right parenthesis times g left parenthesis x right parenthesis end style , maka diperoleh perhitungan 

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell 3 times left parenthesis x squared minus 3 right parenthesis minus left parenthesis x squared minus 3 right parenthesis times left parenthesis x cubed minus 4 x squared minus 5 x plus 2 right parenthesis end cell row blank equals cell 3 x squared minus 9 minus x squared times left parenthesis x cubed minus 4 x squared minus 5 x plus 2 right parenthesis plus 3 times left parenthesis x cubed minus 4 x squared minus 5 x plus 2 right parenthesis end cell row blank equals cell 3 x squared minus 9 minus x to the power of 5 plus 4 x to the power of 4 plus 5 x cubed minus 2 x squared plus 3 x cubed minus 12 x squared minus 15 x plus 6 end cell row blank equals cell negative x to the power of 5 plus 4 x to the power of 4 plus 8 x cubed minus 11 x squared minus 15 x minus 3 end cell end table end style 

Dengan demikian, diperoleh Error converting from MathML to accessible text..

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Roboguru

Diketahui polinomial f(x)=x2−3 dan g(x)=x3−4x2−5x+2. Jika h(x)=3f(x)−f(x)⋅g(x), tentukan derajat polinomial h(x).

Pembahasan Soal:

Polinomial begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus 3 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x cubed minus 4 x squared minus 5 x plus 2 end style

begin mathsize 14px style h left parenthesis x right parenthesis equals 3 f left parenthesis x right parenthesis minus f left parenthesis x right parenthesis times g left parenthesis x right parenthesis end style 
Maka 

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 3 times left parenthesis x squared minus 3 right parenthesis minus left parenthesis x squared minus 3 right parenthesis times left parenthesis x cubed minus 4 x squared minus 5 x plus 2 right parenthesis end cell row blank equals cell 3 x squared minus 9 minus x squared times left parenthesis x cubed minus 4 x squared minus 5 x plus 2 right parenthesis plus 3 times left parenthesis x cubed minus 4 x squared minus 5 x plus 2 right parenthesis end cell row blank equals cell 3 x squared minus 9 minus x to the power of 5 plus 4 x to the power of 4 plus 5 x cubed minus 2 x squared plus 3 x cubed minus 12 x squared minus 15 x plus 6 end cell row blank equals cell negative x to the power of 5 plus 4 x to the power of 4 plus 8 x cubed minus 11 x squared minus 15 x minus 3 end cell end table end style 

Karena Error converting from MathML to accessible text. , pangkat tertinggi begin mathsize 14px style x end style adalah 5. Maka polinomial begin mathsize 14px style h left parenthesis x right parenthesis end style berderajat 5.

0

Roboguru

Diketahui polinomial a,b, dancdengan . Nilai polinomial  untuk x=4 adalah ...

Pembahasan Soal:

Diketahui begin mathsize 14px style a open parentheses 4 close parentheses equals negative 6 comma space b open parentheses 4 close parentheses equals negative 2 comma space c open parentheses 4 close parentheses equals 13 end style, dan begin mathsize 14px style p open parentheses x close parentheses equals a open parentheses x close parentheses cross times b open parentheses x close parentheses minus c open parentheses x close parentheses end style, maka:

begin mathsize 14px style p open parentheses x close parentheses equals a open parentheses x close parentheses cross times b open parentheses x close parentheses minus c open parentheses x close parentheses p open parentheses 4 close parentheses equals a open parentheses 4 close parentheses cross times b open parentheses 4 close parentheses minus c open parentheses 4 close parentheses p left parenthesis 4 right parenthesis equals open parentheses negative 6 close parentheses cross times open parentheses negative 2 close parentheses minus 13 p open parentheses 4 close parentheses equals 12 minus 13 p open parentheses 4 close parentheses equals negative 1 end style 

Jadi, jawaban yang benar adalah B.

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Roboguru

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