Pertanyaan

Diketahuipolinomial f ( x ) = x 2 − 4 x + 2 dan g ( x ) = x 3 − 3 x 2 − 2 x + 1 . Jika h ( x ) = 2 f 2 ( x ) − f ( x ) × g ( x ) , tentukan: c. koefisien x 3 dari polinomial h ( x ) .

Diketahui polinomial  dan .

Jika , tentukan:

c. koefisien  dari polinomial 

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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Pembahasan

Diketahuipolinomial dan . Fungsi . Bentuk kuadrat fungsi dapat dihitung seperti berikut : Bentuk perkalian fungsi adalah : Oleh karena itu, dapat kita tuliskan sebagai berikut. Dari hasil diatas bisa dilihat bahwa koefisien dari polinomial adalah .

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.

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