x^8+x^7+1 x^3+4x^2-19x+24 (x+1)(x+3)(x+5)(x+7)+15 x^3+6x^2+11x+6

0 bình luận về “x^8+x^7+1 x^3+4x^2-19x+24 (x+1)(x+3)(x+5)(x+7)+15 x^3+6x^2+11x+6”

1. Đáp án:

   a, `x^8 + x^7 + 1`

   ` = x^8 + x^7 – x^6 + x^6 + 1`

   `= (x^8 + x^7 + x^6) – (x^6 – 1)`

   `= x^6 . (x^2 + x + 1) – (x^3 – 1)(x^3 + 1)`

   `= x^6 .(x^2 + x + 1) – (x – 1)(x^2 + x + 1)(x^3 + 1)`

   ` = x^6 .(x^2 + x + 1) – (x^2 + x + 1)(x^4 – x^3 + x – 1)`

   ` = (x^2 + x + 1)(x^6 – x^4 + x^3 – x + 1)`

   b, `x^3 + 4x^2 – 29x + 24`

   ` = (x^3 – x^2) + (5x^2 – 5x) – (24x – 24)`

   `= x^2 . (x – 1) + 5x . (x – 1) – 24.(x – 1)`

   `=(x – 1)(x^2 + 5x – 24)`

   `=(x – 1)(x^2 – 3x + 8x – 24)`

   `=(x – 1)[x.(x – 3) + 8.(x – 3)]`

   `=(x – 1)(x – 3)(x + 8)`

   c, `A = (x + 1)(x + 3)(x + 5)(x + 7) + 15`

   `= [(x + 1)(x + 7)].[(x + 3)(x + 5)] + 15`

   `= (x^2 + x + 7x + 7)(x^2 + 3x + 5x + 15) + 15`

   `= (x^2 + 8x + 7)(x^2 + 8x + 15) + 15`

   Đặt `t = x^2 + 8x + 11`

   `=> A = (t – 4)(t + 4) + 15`

   `= t^2 – 16 + 15`

   `= t^2 – 1`

   `= (t – 1)(t + 1)`

   `=> A = (x^2 + 8x + 11 – 1)(x^2 + 8x + 11 + 1)`

   `=> A = (x^2 + 8x + 10)(x^2 + 8x + 12)`

   d, `x^3 + 6x^2 + 11x + 6`

   `= (x^3 + x^2) + (5x^2 + 5x) + (6x + 6)`

   `= x^2 . (x + 1) + 5x.(x + 1) + 6.(x + 1)`

   `= (x + 1)(x^2 + 5x + 6)`

   `= (x + 1)[(x^2 + 2x) + (3x + 6)]`

   `=(x + 1)[x.(x + 2) + 3.(x + 2)]`

   `=(x + 1)(x + 2)(x + 3)`

   Giải thích các bước giải:

     

   Trả lời

2. `a,x^8 + x^7 + 1`

   `= x^8 + x^7 – x^6 + x^6 + 1`

   `= x^6( x^2 + x +1) – [ ( x^3)^2 – 1]`

   `= x^6( x^2 + x +1) – ( x^3 – 1)( x^3 + 1)`

   `= ( x^2 + x +1)[x^6 – ( x -1)( x^3 + 1)]`

   `= ( x^2 + x +1)[ x^6 – ( x^4 + x – x^3 – 1)`

   `= ( x^2 + x +1)( x^6 – x^4 – x + x^3 – 1)`

   `b,x^3+4x^2-19x+24`

   `= x^3-x^2+5x^2-5x-24x+24`

   `=x^2(x-1)+5x(x-1)-24(x-1)`

   `=(x-1)(x^2+5x-24)`

   `=(x-1)(x^2+8x-3x-24)`

   `=(x-1)(x+8)(x-3)`

   `c,(x+1)(x+3)(x+5)(x+7)+15`

   `= (x+1 ) (x+7)(x+3)(x+5)+15`

   `=(x^2+8x+7)(x^2+8x+15)+15`

   Ta đặt `x^2+8x+11=a`

   Ta có :

   `(a-4)(a+4)+15`

   `=a^2-16+15`

   `=a^2-1`

   `=(a-1)(a+1)`

   `⇒ (x^2+8x+11-1)(x^2+8x+11+1)`

   `=(x^2+8x+10)(x^2+8x+12)` 

   `d,x^3 + 6x^2 + 11x + 6`

   `= (x^3 + x^2) + (5x^2 + 5x) + (6x + 6)`

   `= x^2(x + 1) + 5x(x + 1) + 6(x + 1)`

   `= (x^2 + 5x + 6)(x + 1)`

   `= (x^2 + 2x + 3x + 6)(x + 1)`

   `= (x + 3)(x + 2)(x + 1)`

   Xin hay nhất !

   Trả lời