RoboguruRoboguru
SD

Faktor dari x5−1x3−1​ adalah ....

Pertanyaan

Faktor dari begin mathsize 14px style fraction numerator x cubed minus 1 over denominator x to the power of 5 minus 1 end fraction end style adalah ....

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

faktor dari begin mathsize 14px style fraction numerator x cubed minus 1 over denominator x to the power of 5 minus 1 end fraction end style adalah begin mathsize 14px style fraction numerator open parentheses x squared plus x plus 1 close parentheses over denominator open parentheses x to the power of 4 plus x cubed plus x squared plus x plus 1 close parentheses end fraction end style.

Pembahasan

Untuk mempermudah penyelesaian, kita faktorkan bagian pembilang terlebih dahulu.

Untuk mencari faktor dari begin mathsize 14px style x cubed minus 1 end style, kita coba pilih begin mathsize 14px style x equals 1 end style. Dengan metode Horner, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell long division with stack on the left by table row 1 0 0 cell negative 1 end cell row blank 1 1 1 end table yields table row 1 1 1 cell space 0 end cell end table pile 1 end pile end long division end cell row cell Hasil space bagi end cell equals cell x squared plus x plus 1 end cell row Sisa equals 0 end table end style 

Karena sisa pembagian bernilai nol, maka begin mathsize 14px style x minus 1 end style adalah faktor dari begin mathsize 14px style x cubed minus 1 end style. Sementara itu, begin mathsize 14px style x squared plus x plus 1 end style tidak dapat difaktorkan. Jadi, faktor dari begin mathsize 14px style x cubed minus 1 end style adalah begin mathsize 14px style x minus 1 end style dan begin mathsize 14px style x squared plus x plus 1 end style.

Selanjutnya, kita faktorkan bagian penyebut. Untuk mencari faktor dari begin mathsize 14px style x to the power of 5 minus 1 end style, kita coba pilih begin mathsize 14px style x equals 1 end style. Dengan metode Horner, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell long division with stack on the left by table row 1 0 0 0 0 cell negative 1 end cell row blank 1 1 1 1 1 end table yields table row 1 1 1 1 1 0 end table pile 1 end pile end long division end cell row cell Hasil space bagi end cell equals cell x to the power of 4 plus x cubed plus x squared plus x plus 1 end cell row Sisa equals 0 end table end style 

Karena sisa pembagian bernilai nol, maka begin mathsize 14px style x minus 1 end style adalah faktor dari begin mathsize 14px style x to the power of 5 minus 1 end style. Sementara itu, begin mathsize 14px style x to the power of 4 plus x cubed plus x squared plus x plus 1 end style tidak dapat difaktorkan. Jadi, faktor dari begin mathsize 14px style x to the power of 5 minus 1 end style adalah begin mathsize 14px style x minus 1 end style dan begin mathsize 14px style x to the power of 4 plus x cubed plus x squared plus x plus 1 end style.

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x cubed minus 1 over denominator x to the power of 5 minus 1 end fraction end cell equals cell fraction numerator up diagonal strike open parentheses x minus 1 close parentheses end strike open parentheses x squared plus x plus 1 close parentheses over denominator up diagonal strike open parentheses x minus 1 close parentheses end strike open parentheses x to the power of 4 plus x cubed plus x squared plus x plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses x squared plus x plus 1 close parentheses over denominator open parentheses x to the power of 4 plus x cubed plus x squared plus x plus 1 close parentheses end fraction end cell end table end style 

Jadi, faktor dari begin mathsize 14px style fraction numerator x cubed minus 1 over denominator x to the power of 5 minus 1 end fraction end style adalah begin mathsize 14px style fraction numerator open parentheses x squared plus x plus 1 close parentheses over denominator open parentheses x to the power of 4 plus x cubed plus x squared plus x plus 1 close parentheses end fraction end style.

14

0.0 (0 rating)

Pertanyaan serupa

Diberikan polinomial f(x)=x4−2x3−13x2+14x+24.  Jika faktor-faktor rasional dari f(x) adalah (x+a), (x−b), (x +c), (x−d) dengan 0<a<b<c<d, maka nilai dari a⋅b⋅c⋅d adalah ….

108

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia