Question

phân tích các đa thức sau thành nhân tử:

a, x³ -3x² -4x+12

b, x⁴ -5x² +4

c, (x+y+z)³ -x³ -y³ -z³

Answer 1

a)\(x^3-3x^2-4x+12\)

\(=\left(x^3-3x^2\right)-\left(4x-12\right)\)

\(=\left(x-3\right)\left(x^2-4\right)\)

\(=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)

b) \(x^4-5x^2+4\)

\(=\left(x^4-4x^2\right)-\left(x^2-4\right)\)

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

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

Answer 2

ban kia lam dung roi do

k tui nha

thanks

Answer 3

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

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

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

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

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

Answer 4

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

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

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

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

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