Question

Phân tích các đa thức sau thành nhân tử

a)xy+y-2x-2                                 d)xy+xz+y²+yz

b)x+x+x+1                                  e)xy+1+x+y

c)x³-3x²+3x-9                             f)x²+xy+xz-x-y-z

Answer 1

Câu a:

Cách 1:
\(xy+y-2x-2\)
\(\Leftrightarrow\left(xy+y\right)-\left(2x+2\right)\)
\(\Leftrightarrow y\left(x+1\right)-2\left(x+1\right)\)
\(\Leftrightarrow\left(x+1\right)\left(y-2\right)\)

Cách 2:
\(xy+y-2x-2\)
\(\Leftrightarrow\left(xy-2x\right)+\left(y-2\right)\)
\(\Leftrightarrow x\left(y-2\right)+\left(y-2\right)\)
\(\Leftrightarrow\left(x+1\right)\left(y-2\right)\)

Answer 2

a)xy+y-2x-2

y(x + 1) - 2(x + 1)

<=> (y - 2)(x + 1)

b) x + x + x + 1

<=> 3x + 1

c)x³-3x²+3x-9 

<=>(x - 3 ) ³

d)xy+xz+y²+yz

<=> x(y + z) + y(y + z)

<=> (x + y)(y + z)

f)x²+xy+xz-x-y-z

<=> x(x - y -z +1