Question

phân tích đa thức sau thành nhân tử :

a, (x+y+z)² -x³-y³-z³

b, x⁴+2010x²+2009x+2010

Answer 1

sửa đề:\(\left(x+y+z\right)^3-x^3-y^3-z^3\)

giải:

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

Answer 2

b,W = \(x^4+x^2+1+2009x^2+2009x+2009\)

\(=\left(x^4+2x^2+1\right)-x^2+2009\left(x^2+x+1\right)\)

\(=\left(x^2+1\right)^2-x^2+2009\left(x^2+x+1\right)\)

\(=\left(x^2+1-x\right)\left(x^2+1+x\right)+2009\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2010\right)\)

Answer 3

b, x⁴-x+2010x²+2009x+x+2010

=(x⁴-x)+(2010x²2010x+2010)

=x(x³-1)+2010(x²+x+1)

=x(x-1)(x²+x+1)+2010(x²+x+1)

=(x²+x+1)[x(x-1)+2010]

=(x²+x+1)(x²-x+2010)