Question

Phân tích các đa thức sau thành nhân tử:

a) x² + 2x + 1 + x + 1

b) y² + xy + x + 2y + 1

c) xy - y - 2x - 2

d) x³ + x² + x + 1

e) xy + xz + y² + yz

Answer 1

a, x²+2x+1+x+1

=(x²+2x+2)+x

=(x²+2x+1²)+x

=(x+1)²+x

=(2x+1)²

=(2x-1).(2x+1 )

Answer 2

c,xy-y-2x-2

=(xy-2x)-(y-2)

=x.(y-2)-(y-2) 

=(y-2).x

e,xy+xz+y²+yz

=(xy+y²)+(xz+yz)

=y.(x+y)+z.(x+y)

=(x+y).(y+z)

d,x³+x²+x+1

=(x³+x²)+(x+1)

=x².(x+1)+(x+1)

=x².(x+1)

b,y²+xy+x+2y+1

=(y²+2y)+(xy+x+1)

=y.(y+2) + x.(y+2)

=(y+2).(y+x)

Answer 3

\(x^2-2x+1+x+1\)

\(=\left(x+1\right)^2+\left(x+1\right)\)

\(=\left(x+1\right)\left(x+1+1\right)\)

\(=\left(x+1\right)\left(x+2\right)\)