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

Pertanyaan

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.

Jika begin mathsize 14px style h left parenthesis x right parenthesis equals 2 f squared left parenthesis x right parenthesis minus f left parenthesis x right parenthesis cross times g left parenthesis x right parenthesis end style, tentukan:

c. koefisien begin mathsize 14px style x cubed end style dari polinomial undefined

Pembahasan Video:

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 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 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   
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.

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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