Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a, x4 + 2x3 +x2 = x4 +x3 +x3 +x2 =(x4+x3 )+(x3 +x2 ) =x3(x +1 ) + x2 (x+1 ) =(x+1)(x3+x2)
a) x4 + 2x3 + x2
= x2(x2 + 2x + 1)
= x2(x + 1)2
= [x(x + 1)]2
= (x2 + x)2
b) 5x3 - 10xy + 5y2 - 20z2
= 5(x3 - 2xy + y2 - 4z2)
c) x2y - xy2 + x3 - y3
= xy(x - y) + (x - y)(x2 + xy + y2)
= (x - y)(x2 + 2xy + y2)
= (x - y)(x + y)2
d) x2 - xy + 4x - 2y + 4
= (x2 + 4x + 4) - (xy + 2y)
= (x + 2)2 - y(x + 2)
= (x + 2)(x + 2 - y)
d) x2 - x - 6
= x2 - 3x + 2x - 6
= x(x - 3) + 2(x - 3)
= (x + 2)(x - 3)
f) 3x2 - 5x - 8
= 3x2 + 3x - 8x - 8
= 3x(x + 1) - 8(x + 1)
= (3x - 8)(x + 1)
g) x3 + 3x2 + 6x + 4
= (x3 + 3x2 + 3x + 1) + (3x + 3)
= (x + 1)3 + 3(x + 1)
= (x + 1)[(x + 1)2 + 3]
h) 3x3 - 5x2 - 6x + 8
= 3x3 - 3x2 - 2x2 - 6x + 8
= 3x3 - 3x2 - 2x2 + 2x - 8x + 8
= 3x2(x - 1) - 2x(x - 1) - 8(x - 1)
= (3x2 - 2x - 8)(x - 1)
a) \(x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
b) \(5x^2-10xy+5y^2-20z^2\) (đã sửa đề)
\(=5\left[\left(x^2-2xy+y^2\right)-4z^2\right]\)
\(=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)
\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)
c) \(x^2y-xy^2+x^3-y^3\)
\(=xy\left(x-y\right)+\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=\left(x-y\right)\left(x^2+2xy+y^2\right)\)
\(=\left(x-y\right)\left(x+y\right)^2\)
d) \(x^2-xy+4x-2y+4\)
\(=\left(x^2+4x+4\right)-\left(xy+2y\right)\)
\(=\left(x+2\right)^2-y\left(x+2\right)\)
\(=\left(x+2\right)\left(x-y+2\right)\)
e) \(x^2-x-6=\left(x+2\right)\left(x-3\right)\)
f) \(3x^2-5x-8\)
\(=\left(3x^2+3x\right)-\left(8x+8\right)\)
\(=3x\left(x+1\right)-8\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-8\right)\)
\(B=7x^2-7xy-5x+5y\)
\(=7x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(7x-5\right)\)
\(E=x^2+7x+12\)
\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
\(F=x^2-9x+18\)
\(=x^2-3x-6x+18\)
\(=x\left(x-3\right)-6\left(x-3\right)\)
\(=\left(x-3\right)\left(x-6\right)\)
\(H=8x^2-2x-1\)
\(=8x^2-4x+2x-1\)
\(=4x\left(2x-1\right)+\left(2x-1\right)\)
\(=\left(2x-1\right)\left(4x+1\right)\)
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@@