Roboguru

Diketahui  dan . Jika , nilai  adalah...

Pertanyaan

Diketahui begin mathsize 14px style straight f open parentheses x close parentheses equals 3 x to the power of 4 minus 2 x cubed plus 4 x squared minus 6 end style dan begin mathsize 14px style straight g open parentheses x close parentheses equals 4 x to the power of 4 minus x cubed minus 5 x squared plus 3 x plus 15 end style. Jika begin mathsize 14px style straight h open parentheses x close parentheses equals straight f open parentheses x close parentheses minus straight g open parentheses x close parentheses end style, nilai begin mathsize 14px style straight h open parentheses 2 close parentheses end style adalah...

  1. begin mathsize 14px style 15 end style 

  2. begin mathsize 14px style 12 end style 

  3. begin mathsize 14px style negative 8 end style 

  4. begin mathsize 14px style negative 12 end style 

  5. begin mathsize 14px style negative 15 end style  

Pembahasan Soal:

Berdasarkan soal di atas, maka hasil pengurangan dua suku banyak tersebut sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight h open parentheses x close parentheses end cell equals cell straight f open parentheses x close parentheses minus straight g open parentheses x close parentheses end cell row blank equals cell 3 x to the power of 4 minus 2 x cubed plus 4 x squared minus 6 minus open parentheses 4 x to the power of 4 minus x cubed minus 5 x squared plus 3 x plus 15 close parentheses end cell row blank equals cell 3 x to the power of 4 minus 2 x cubed plus 4 x squared minus 6 minus 4 x to the power of 4 plus x cubed plus 5 x squared minus 3 x minus 15 end cell row blank equals cell negative x to the power of 4 minus x cubed plus 9 x squared minus 3 x minus 21 end cell end table end style

Kemudian substitusi nilai begin mathsize 14px style x equals 2 end style, sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight h open parentheses 2 close parentheses end cell equals cell negative open parentheses 2 close parentheses to the power of 4 minus open parentheses 2 close parentheses cubed plus 9 open parentheses 2 close parentheses squared minus 3 open parentheses 2 close parentheses minus 21 end cell row blank equals cell negative 16 minus 8 plus 36 minus 6 minus 21 end cell row blank equals cell negative 15 end cell end table end style 

Oleh karena itu, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

K. Putri

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Terakhir diupdate 29 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui polinomial  dengan . Jika , nilai  adalah ...

Pembahasan Soal:

Diketahui begin mathsize 14px style p open parentheses negative 5 close parentheses equals 4 comma space q open parentheses negative 5 close parentheses equals negative 3 end style, dan begin mathsize 14px style p open parentheses x close parentheses equals 3 q open parentheses x close parentheses minus 2 r open parentheses x close parentheses end style, maka:

begin mathsize 14px style space space space space space space space space space space space space space space p left parenthesis x right parenthesis equals 3 q left parenthesis x right parenthesis minus 2 r left parenthesis x right parenthesis space space space space space space space space space space space p left parenthesis negative 5 right parenthesis equals 3 q left parenthesis negative 5 right parenthesis minus 2 r left parenthesis negative 5 right parenthesis space space space space space space space space space space space space space space space space space space space 4 equals 3 open parentheses negative 3 close parentheses minus 2 r open parentheses negative 5 close parentheses space space space space space space space space space space space space space space space space space space space 4 equals negative 9 minus 2 r open parentheses negative 5 close parentheses minus 9 minus 2 r left parenthesis negative 5 right parenthesis equals 4 space space space space space space minus 2 r open parentheses negative 5 close parentheses equals 4 plus 9 space space space space space space minus 2 r open parentheses negative 5 close parentheses equals 13 space space space space space space space space space space space r open parentheses negative 5 close parentheses equals fraction numerator 13 over denominator negative 2 end fraction space space space space space space space space space space space r open parentheses negative 5 close parentheses equals negative 6 comma 5 end style 

Jadi, jawaban yang benar adalah C.

Roboguru

Diketahui nilai polinomial  berturut-turut adalah . Jika , nilai

Pembahasan Soal:

Diketahui begin mathsize 14px style p open parentheses 6 close parentheses equals negative 4 end stylebegin mathsize 14px style q open parentheses 6 close parentheses equals 8 end style, dan begin mathsize 14px style r open parentheses x close parentheses equals 3 p open parentheses x close parentheses minus q open parentheses x close parentheses end style, maka:

begin mathsize 14px style r open parentheses x close parentheses equals 3 p open parentheses x close parentheses minus q open parentheses x close parentheses r open parentheses 6 close parentheses equals 3 p open parentheses 6 close parentheses minus q open parentheses 6 close parentheses r open parentheses 6 close parentheses equals 3 open parentheses negative 4 close parentheses minus 8 r open parentheses 6 close parentheses equals negative 12 minus 8 r open parentheses 6 close parentheses equals negative 20 end style 

Jadi, jawaban yang benar adalah A.

Roboguru

Diketahui polinomial  dan . Jika dan, nilai  adalah ...

Pembahasan Soal:

Diketahui begin mathsize 14px style p open parentheses x close parentheses equals 4 x cubed minus 2 x squared plus 1 comma space q open parentheses x close parentheses equals x to the power of 4 minus n x squared plus 2 comma space r open parentheses x close parentheses equals p open parentheses x close parentheses minus q open parentheses x close parentheses end style, dan begin mathsize 14px style r open parentheses 2 close parentheses equals 39 end style, maka:

 size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px p begin mathsize 14px style left parenthesis x right parenthesis end style size 14px minus size 14px q begin mathsize 14px style left parenthesis x right parenthesis end style size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals begin mathsize 14px style left parenthesis 4 x cubed minus 2 x squared plus 1 right parenthesis end style size 14px minus begin mathsize 14px style left parenthesis x to the power of 4 minus n x squared plus 2 right parenthesis end style size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px 4 size 14px x to the power of size 14px 3 size 14px minus size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px 1 size 14px minus size 14px x to the power of size 14px 4 size 14px plus size 14px n size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px minus size 14px x to the power of size 14px 4 size 14px plus size 14px 4 size 14px x to the power of size 14px 3 size 14px plus size 14px n size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px 1 size 14px minus size 14px 2 size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px minus size 14px x to the power of size 14px 4 size 14px plus size 14px 4 size 14px x to the power of size 14px 3 size 14px plus begin mathsize 14px style left parenthesis n minus 2 right parenthesis end style size 14px x to the power of size 14px 2 size 14px minus size 14px 1    

Sehingga:

begin mathsize 14px style space space space space r open parentheses x close parentheses equals negative x to the power of 4 plus 4 x cubed plus open parentheses n minus 2 close parentheses x squared minus 1 space space space space r open parentheses 2 close parentheses equals negative open parentheses 2 close parentheses to the power of 4 plus 4 open parentheses 2 close parentheses cubed plus open parentheses n minus 2 close parentheses open parentheses 2 close parentheses squared minus 1 space space space space space space 39 equals negative 16 plus 4 left parenthesis 8 right parenthesis plus left parenthesis n minus 2 right parenthesis open parentheses 4 close parentheses minus 1 space space space space space space 39 equals negative 16 plus 32 plus 4 n minus 8 minus 1 space space space space space space 39 equals 4 n plus 7 4 n plus 7 equals 39 space space space space space 4 n equals 39 minus 7 space space space space space 4 n equals 32 space space space space space space space n equals 32 over 4 space space space space space space space n equals 8 end style 

Jadi, jawaban yang benar adalah A.

Roboguru

Diketahui polinomial dengan . Nilai polinomial  untuk  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.

Roboguru

Diketahui polinomial   dan . Jika   adalah . . ..

Pembahasan Soal:

Diketahui: begin mathsize 14px style p open parentheses x close parentheses equals x to the power of 4 minus 2 x cubed plus 4 x squared minus 8 end style dan begin mathsize 14px style q open parentheses x close parentheses equals 2 x to the power of 4 minus x cubed minus 5 x squared plus 3 x plus 12 end style 

Maka,

begin mathsize 14px style r open parentheses x close parentheses equals p open parentheses x close parentheses minus q open parentheses x close parentheses r open parentheses x close parentheses equals open parentheses x to the power of 4 minus 2 x cubed plus 4 x squared minus 8 close parentheses minus open parentheses 2 x to the power of 4 minus x cubed minus 5 x squared plus 3 x plus 12 close parentheses r open parentheses x close parentheses equals x to the power of 4 minus 2 x cubed plus 4 x squared minus 8 minus 2 x to the power of 4 plus x cubed plus 5 x squared minus 3 x minus 12 r open parentheses x close parentheses equals negative x to the power of 4 minus x cubed plus 9 x squared minus 3 x minus 20 end style  

Sehingga,

begin mathsize 14px style r left parenthesis x right parenthesis equals negative x to the power of 4 minus x cubed plus 9 x squared minus 3 x minus 20 r left parenthesis 2 right parenthesis equals negative left parenthesis 2 right parenthesis to the power of 4 minus left parenthesis 2 right parenthesis cubed plus 9 left parenthesis 2 right parenthesis squared minus 3 left parenthesis 2 right parenthesis minus 20 r left parenthesis 2 right parenthesis equals negative 16 minus 8 plus 36 minus 6 minus 20 r left parenthesis 2 right parenthesis equals negative 14 end style 

Jadi, jawaban yang benar adalah D.

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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