Question

Phân tích đa thức thành nhân tử:
a) x^4 - 3x^3 - x +3
b) 3x + 3y - x^2 - 2xy - y^2
c) x^2 - 7x + 6
d) x^3 - x^2y - xy^2 + y^3

Answer 1

a) Linh cảm câu này sai đề :)

b) \(3x+3y-x^2-2xy-y^2=3\left(x+y\right)-\left(x+y\right)^2=\left(x+y\right)\left(3-x-y\right)\)

c) \(x^2-7x+6=x^2-x-6x+6=x\left(x-1\right)-6\left(x-1\right)=\left(x-1\right)\left(x-6\right)\)

d) \(x^3-x^2y-xy^2+y^3=x^2\left(x-y\right)-y^2\left(x-y\right)=\left(x-y\right)^2\left(x+y\right)\)

Answer 2

a: \(=x^3\left(x-3\right)-\left(x-3\right)=\left(x-3\right)\left(x-1\right)\left(x^2+x+1\right)\)

b: \(=3\left(x+y\right)-\left(x+y\right)^2\)

\(=\left(x+y\right)\left(3-x-y\right)\)

c: \(=\left(x-1\right)\left(x-6\right)\)

d: \(=\left(x+y\right)\left(x^2-xy+y^2\right)-xy\left(x+y\right)\)

\(=\left(x+y\right)\left(x-y\right)^2\)