1, x^4 +3x^3 +x^2 -12x -20 2, x^3 -10x -12 3, 4x^12 -12x +1 4, x^8 +x +1 5, x^8 +x^7 +1 6, 4.x^4.y^4 +1 7, (x^2+x)^2 + 4x(x+1) -12
4.$(x^8-x^2)+(x^2+x+1)$ $x^2(x-1)(x^2+x+1)(x^3+1)+(x^2+x+1)$ =.... 5.$x^8+x^7+1$ =$x^8+x^7+x^6-x^6+x^5-x^5+.....+x^2-x^2+1$ =$x^6(x^2+x+1)-x^4(x^2+x+1)+x^3(x^2+x+1)-x(x^2+x+1) =$(x^2+x+1)(x^6-x^4+x^3-x+1)$
1) $x^4 +3x^3 +x^2 -12x -20$ $= x^4 - 4x^2 + 3x^3 - 12x + 5x^2 - 20$ $= x^2(x^2 - 4) + 3x(x^2 - 4) + 5(x^2 - 4)$ $= (x^2 + 3x + 5)(x^2 - 4)$ $= (x^2 + 3x + 5)(x - 2)(x + 2)$ 2) $x^3 - 10x - 12$ $= x^3 + 2x^2 - 2x^2 - 4x - 6x - 12$ $= x^2(x + 2) - 2x(x + 2) - 6(x + 2)$ $= (x^2 - 2x - 6)(x + 2)$ 3) Đề sai 4) $x^8 + x + 1$ $= x^8 + x^7 + x^6 - x^7 - x^6 - x^5 + x^5 + x^4 + x^3 - x^4 - x^3 - x^2 + x^2 + x + 1$ $= x^6(x^2 + x + 1) - x^5(x^2 + x + 1) + x^3(x^2 + x + 1) - x^2(x^2 + x + 1) + x^2 + x + 1$ $= (x^6 - x^5 + x^3 - x^2 + 1)(x^2 + x + 1)$ 5) $x^8 + x^7 + 1$ $= x^8 + x^7 + x^6 - x^6 - x^5 - x^4 + x^5 + x^4 + x^3 - x^3 - x^2 - x + x^2 + x + 1$ $= x^6(x^2 + x + 1) - x^4(x^2 + x + 1) + x^3(x^2 + x + 1) - x(x^2 + x + 1) + (x^2 + x + 1)$ $= (x^6 - x^4 + x^3 - x + 1)(x^2 + x + 1)$ 6) $4x^4y^4 + 1$ $= 4x^4y^4 + 4x^2y^2 + 1 - 4x^2y^2$ $= (2x^2y^2)^2 + 2.(2x^2y^2) + 1 - 4x^2y^2$ $= (2x^2y^2 + 1)^2 - (2xy)^2$ $= (2x^2y^2 - 2xy + 1)(2x^2y^2 + 2xy + 1)$ 7) Đặt $t = x^2 + x$, ta có: $(x^2 + x)^2 + 4x(x + 1) - 12$ $= t^2 + 4t - 12$ $= t^2 - 2t + 6t - 12$ $= (t - 2)t + (t - 2)6$ $= (t - 2)(t + 6)$ $= (x^2 + x - 2)(x^2 + x + 6)$ $= (x^2 -x + 2x - 2)(x^2 + x + 6)$ $= (x(x - 1) + 2(x - 1))(x^2 + x + 6)$ $= (x + 2)(x - 1)(x^2 + x + 6)$
1) x^4+3x^3+x^2−12x−20 =x^4−4x^2+3x^3−12x+5x^2−20 =x^2(x^2−4)+3x(x^2−4)+5(x^2−4) =(x^2+3x+5)(x^2−4) =(x^2+3x+5)(x−2)(x+2) 2) x^3−10x−12 =x^3+2x^2−2x^2−4x−6x−12 =x^2(x+2)−2x(x+2)−6(x+2) =(x^2−2x−6)(x+2) 4) x^8+x+1 =x^8+x^7+x^6−x^7−x^6−x^5+x^5+x^4+x^3−x^4 − x^3−x^2+x^2+x+1 =x^6(x^2+x+1)−x^5(x^2+x+1)+x^3(x^2+x+1)−x^2(x^2+x+1)+x^2+x+1 =(x^6−x^5+x^3−x^2+1)(x^2+x+1) 5) x^8+x^7+1 =x^8+x^7+x^6−x^6−x^5−x^4+x^5+x^4 + x^3−x^3−x^2−x+x^2+x+1 =x^6(x^2+x+1)−x^4(x^2+x+1)+x^3(x^2+x+1)−x(x^2+x+1)+(x^2+x+1) =(x^6−x^4+x^3−x+1)(x^2+x+1) 6) 4x4y4+1 =4x^4y^4+4x^2y^2+1−4x^2y^2 =(2x2y2)2+2.(2x^2y^2)+1−4x^2y^2 =(2x^2y^2+1)2−(2xy)2 =(2x^2y^2−2xy+1)(2x2y2+2xy+1) 7) Đặt t=x^2+x, ta có: (x^2+x)2+4x(x+1)−12 =t2+4t−12 =t2−2t+6t−12 =(t−2)t+(t−2)6 =(t−2)(t+6) =(x^2+x−2)(x^2+x+6) =(x^2−x+2x−2)(x^2+x+6) =[x(x−1)+2(x−1)](x^2+x+6) =(x+2)(x−1)(x^2+x+6)
1. $x^4 +3x^3 +x^2 -12x -20 = (x - 2)(x + 2)(x^2 + 3x + 5)$ 2. $x^3 -10x -12 = (x + 2)(x^2 - 2x - 6)$ 3. Đề lỗi rồi bạn ơi 4. $x^8 +x +1 = (x^2 + x + 1)(x^6 - x^5 + x^3 - x^2 +1)$ 5. $ x^8 +x^7 +1 = (x^2 + x + 1)(x^6 - x^4 + x^3 - x + 1)$ 6. $4.x^4.y^4 +1 = (2x^2y^2 - 2xy + 1)(2x^2y^2 + 2xy + 1)$ 7. $(x^2+x)^2 + 4x(x+1) -12 = (x - 1)(x + 2)(x^2 + x + 6)$