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 20/07/2021 Bởi Cora 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
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: Bình luận
`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 ! Bình luận
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:
`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 !