Register Now

Login

Lost Password

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: Phân tích thành nhân tử x^10+x^5+1

Toán Lớp 8: Phân tích thành nhân tử x^10+x^5+1

Comments ( 2 )

  1.     x^[10] + x^5 + 1
    = x^[10] + x^5 + 1 + x² – x² + x – x
    = ( x^[10] – x ) + ( x^5 – x² ) + ( x² + x + 1 )
    = x ( x^9 – 1 ) + x^2 ( x^3 – 1 ) + ( x² + x + 1 )
    = x ( x³ – 1 ) ( x^6 + x³ + 1 ) + x² ( x – 1 ) ( x² + x + 1 ) + ( x² + x + 1 )
    = x ( x – 1 ) ( x² + x + 1 ) ( x^6 + x³ + 1 ) + x² ( x – 1 ) ( x² + x + 1 ) + ( x² + x + 1 )
    = ( x² + x + 1 ) [ x ( x – 1 ) ( x² + x + 1 ) + x² ( x – 1 ) + 1 ]
    = ( x² + x + 1 ) { ( x + 1 ) [ x ( x² + x + 1 ) + x² ] + 1 ]
    = ( x² + x + 1 ) [ ( x + 1 ) ( x³ + x² + x + x² ) + 1 ]
    = ( x² + x + 1 ) [ ( x + 1 ) ( x³ + 2x² + x ) + 1 ]
    = ( x² + x + 1 ) [ ( x + 1 ) . x . ( x² + 2x + 1 ) + 1 ]
    = ( x² + x + 1 ) [ ( x + 1 ) . x . ( x + 1 )² + 1 ]
    = ( x² + x + 1 ) [ x . ( x + 1 )³ + 1 ]

  2. Lời giải và giải thích chi tiết:
    x^10+x^5+1
    =x^10+x^9+x^8-x^9-x^8-x^7+x^7+x^6+x^5-x^6-x^5-x^4+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1
    =x^8(x^2+x+1)-x^7(x^2+x+1)+x^5(x^2+x+1)-x^4(x^2+x+1)+x^3(x^2+x+1)-x(x^2+x+1)+1(x^2+x+1)
    =(x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x+1)

Leave a reply

222-9+11+12:2*14+14 = ? ( )

About Linh