Question

Phân tích đa thức sau thành nhân tử :
a, x^4 + 2x^3 - 4x - 4
b, x^2 - 4xy + 10y^2
c, x^3 - 19x - 30
d, x^3 - 7x - 6
e, x^3 - 5x^2 - 14
Giúp mình với mình đang cần rất gấp ạ

Answer 1

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

\(=x^4-2x^2+2x^3-4x+2x^2-4\)

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

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

b/ \(x^3-19x-30\)

\(=x^3+2x^2-2x^2-4x-15x-30\)

\(=x^2\left(x+2\right)-2x\left(x+2\right)-15\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-2x-15\right)\)

\(=\left(x+2\right)\left(x+3\right)\left(x-5\right)\)

c/ \(x^3-7x-6\)

\(=x^3+x^2-x^2-x-6x-6\)

\(=x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x-6\right)\)

\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)