Phân tích đa thức thành nhân tử:a) x3 + x + 2b) x3 - x - 2c) x3 + 32x - 4d) x3y3 + x2y2 + 4e) x3 + 3x2y - 9xy2 + 5y3g) x4 + x3 + 6x2 + 5x + 5h) x4 - 2x3 - 12x2 + 12x + 36i) x8y8 + x4y4 + 1k) x5 - x4 + x3 - x2 + x + 1l) x5 + x4 - x3 + x2 - x +...
Đọc tiếp
Phân tích đa thức thành nhân tử:
a) x3 + x + 2
b) x3 - x - 2
c) x3 + 32x - 4
d) x3y3 + x2y2 + 4
e) x3 + 3x2y - 9xy2 + 5y3
g) x4 + x3 + 6x2 + 5x + 5
h) x4 - 2x3 - 12x2 + 12x + 36
i) x8y8 + x4y4 + 1
k) x5 - x4 + x3 - x2 + x + 1
l) x5 + x4 - x3 + x2 - x + 2
x3 + x + 2
\(=x^3+x^2-x^2-x+2x+2\)
\(=x^2\left(x+1\right)-x\left(x+1\right)+2\left(x+1\right)\)
\(\left(x+1\right)\left(x^2-x+2\right)\)
c) x3 + 32x - 4
\(=x^3-x^2+4x^2-4x+4x-4\)
\(=x^2\left(x-1\right)+4x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+4x+4\right)\)
\(=\left(x-1\right)\left(x+2^2\right)\)
d)x3y3 + x2y2 + 4
\(=x^3y^3-4xy+x^2y^2-4xy+4\)
\(=xy\left(x^2y^2-4\right)+\left(xy+2\right)^2\)
\(=xy\left(xy-2\right)\left(xy+2\right)+\left(xy+2\right)^2\)
\(=\left(xy+2\right)\left(xy\left(xy-2\right)+xy+2\right)\)
\(=\left(xy+2\right)\left(x^2y^2-2xy+xy+2\right)\)
\(=\left(xy+2\right)\left(x^2y^2-xy+2\right)\)
e) x3 + 3x2y - 9xy2 + 5y3
\(=x^3-3x^2y+3xy^2-y^3+6x^2y-12xy^2+6y^3\)
\(=\left(x-y\right)^3\left(x^2-2xy+y^2\right)\)
\(=\left(x-y\right)^3\left(x-y\right)^2=\left(x-y\right)^2\left(x-y-1\right)\)