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a/ 4x2+x-4x-1
x(4x+1)-(4x+1)
(4x+1)(x-1)
b/(6-11)x2+3
-5x2+3
c/x2-3xy-4xy+12y2
x(x-3y)-4y(x-3y)
(x-3y)(x-4y)
d/(x-y)2+3(x-y)
(x-y+3)(x-y)
e/(2-12)x2+17x-2
-10x2+17x-2
g/x3+x2+2x2+2x+4x+4
x2(x+1)+2x(x+1)+4(x+1)
(x+1)(x2+2x+4)
h/x3+2x2+7x2+14x+12x+24
x2(x+2)+7x(x+2)+12(x+2)
(x+2)(x2+7x+12)
(x+2)(x2+4x+3x+12)
(x+2)(x+4)(x+3)
Giải:
a) 4x2 - 3x - 1 = 4x2 - 4x + x - 1 = 4x(x - 1) + (x -1) = (x - 1)(4x +1)
b) 6x2 - 11x + 3 = 6x2 - 2x - 9x + 3 = 2x(3x - 1) - 3(3x - 1) = (3x - 1)(2x - 3)
c) x2 - 7xy + 12y2 = x2 - 6xy + 9y2 - xy +3y2 = (x - 3y)2 - y(x - 3y) = (x - 3y)( x - 3y - y) = (x - 3y)(x - 4y)
d) x2 - 2xy + y2 + 3x - 3y = (x - y)2 + 3(x - y) = (x - y)(x - y + 3)
e)Sửa đề: x2 → x3
2x3 - 12x2 + 17x - 2 = 2x3 - 4x2 - 8x2 + 16x + x - 2 = (2x2- 8x + 1)(x -2)
f) x3 - 3x + 2 = x3 - x - 2x + 2 = x(x + 1)(x - 1) - 2(x - 1) = (x - 1)(x2 + x - 2) = (x - 1)2(x + 2)
g) x3 + 3x2 + 6x + 4 = x3 + 3x2 + 3x + 1 + 3x + 3 = (x +1)3 + (x + 1) = (x + 1)(x2 + 2x + 4 )
h) x3 + 9x2 + 26x + 24 = x3 + 4x2 + 5x2 + 20x + 6x + 24 = (x + 4)(x2 + 5x + 6) = (x + 4)(x + 3)(x + 2)ư
Chúc bạn học tốt@@
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
đi qua đường vào giúp cho một câu:
\(a^3+b^3+c^3-3abc\)
\(=a^3+3ab\left(a+b\right)+b^3+c^3-3abc-3ab\left(a+b\right)\)
\(=\left(a+b\right)^3+c^3-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(\left(a+b\right)^2+c\left(a+b\right)+c^2\right)-3ab\left(a+b+c\right)\)
\(\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ac\right)\)
==" thui thêm câu nữa mai kiểm tra 1 tiết ùi :D
\(x^2-2xy+y^2+3x-3y-10\)
\(=\left(x-y\right)^2+3\left(x-y\right)-10\)
\(=\left(x-y\right)\left(x-y+3\right)-10\)
Đặt x-y = a, có:
\(a\left(a+3\right)-10\)
\(=a^2+3a-10\)
\(=\left(a+5\right)\left(a-2\right)\)
\(=\left(x-y+5\right)\left(x-y-2\right)\)
e) Sửa đề:
$2x^3-12x^2+17x-2=2x^3-4x^2-8x^2+16x+x-2$
$=2x^2(x-2)-8x(x-2)+(x-2)=(x-2)(2x^2-8x+1)$
f)
$x^3-3x+2=(x^3-x)-(2x-2)=x(x^2-1)-2(x-1)=x(x-1)(x+1)-2(x-1)$
$=(x-1)(x^2+x-2)=(x-1)(x^2-x+2x-2)=(x-1)[x(x-1)+2(x-1)]$
$=(x-1)(x-1)(x+2)=(x-1)^2(x+2)$
g)
$x^3+3x^2=x^2(x+3)$
h)
$x^3+9x^2+26x+24=(x^3+9x^2+27x+27)-x-3$
$=(x+3)^3-(x+3)=(x+3)[(x+3)^2-1]=(x+3)(x+3-1)(x+3+1)$
$=(x+3)(x+2)(x+4)$
a)
$4x^2-3x-1=4x^2-4x+x-1=4x(x-1)+(x-1)=(4x+1)(x-1)$
b)
$6x^2-11x^2=-5x^2$
c)
\(x^2-7xy+12y^2=x^2-4xy-3xy+12y^2\)
\(=x(x-4y)-3y(x-4y)=(x-3y)(x-4y)\)
d)
\(x^2-2xy+y^2+3x-3y=(x^2-2xy+y^2)+(3x-3y)\)
\(=(x-y)^2+3(x-y)=(x-y)(x-y+3)\)