Question

Phân tích các đa thức sau thành nhân tử

a) \(^{ }3xy-6xy^2\) 

b) \(^{ }3x^3+6x^2+3x\)

c) \(^{ }x^3-x^2+2\)

d) \(^{ }x^2+4x+4-y^2\)

e) \(^{ }x^3+4x^2+4x\)

f) \(^{ }x^2+2x+1-9y^2\)

g) \(^{ }6x^2-12x\)

h) \(^{ }x^3+2x^2-x\)

i) \(^{ }x^2-2xy+y^2-9\)

j) \(^{ }x^2+x-6\)

k) \(^{ }2x^3+2x^2y-4xy^2\)

l) \(^{ }x^3-4x^2-12x+27\)

Answer 1

a) \(3xy-6xy^2=3xy\left(1-2y\right)\)

b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)

c) \(x^3-x^2+2\)

d) \(x^2+4x+4-y^2=\left(x^2+4x+4\right)-y^2=\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\)

e) \(x^3+4x^2+4x=x\left(x^2+4x+4\right)=x\left(x+2\right)^2\)

f) \(x^2+2x+1-9y^2=\left(x+1\right)^2-\left(3y\right)^2=\left(x-3y+1\right)\left(x+3y+1\right)\)

g) \(6x^2-12x=6x\left(x-2\right)\)

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

i) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)

Answer 2

k) \(2x^3+2x^2y-4xy^2=2x\left(x^2+xy-2y^2\right)\)

l) \(x^3-7x^2+9x+3x^2-21x+27=x\left(x^2-7x+9\right)+3\left(x^2-7x+9\right)=\left(x+3\right)\left(x^2-7x+9\right)\)