Question

phân tích các đa thức sau thành nhân tử:

a) x⁴+x³-x²+x-2

b) x⁷x²+1

c) xy(x+y)+yz(y+z)+zx(z+x)+3xyz

Answer 1

c)

\(xy\left(x+y\right)+yz\left(y+z\right)+zx\left(z+x\right)+3xyz\\ =x^2y+y^2x+y^2z+z^2y+z^2x+x^2z+3xyz\\ =\left(x^2y+y^2x+xyz\right)+\left(x^2z+z^2x+xyz\right)+\left(y^2z+z^2y+xyz\right)\\= xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(x+y+z\right)\\ =\left(x+y+z\right)\left(xy+xz+yz\right)\)

Answer 2

\(x^4+x^3-x^2+x-2\\ \Leftrightarrow x^4+x^3-2x^2+x^2+x-2\\ \Leftrightarrow\left(x^4+x^3\right)+\left(x^2+x\right)-\left(2x^2-2\right)\\ \Leftrightarrow x^3\left(x+1\right)+x\left(x+1\right)-2\left(x^2-1\right)\\ \Leftrightarrow x^3\left(x+1\right)+x\left(x+1\right)-2\left(x+1\right)\left(x-1\right)\\ \Leftrightarrow x^3\left(x+1\right)+x\left(x+1\right)-\left(x+1\right)\left(2x-2\right)\\ \Leftrightarrow\left(x+1\right)\left(x^3+x-2x+2\right)\\ \Leftrightarrow\left(x+1\right)\left(x^3-x+2\right)\)