Question

Phân tích đa thúc thành nhân tử

a ) x² - 25 + ( x + 5 ).(5 - 2x )

b ) 3x² - 6xy + 3y² - 12z²

c ) x^{3 -} 3x² + 4x - 12

d ) x² - y² + 4x +4

Answer 1

a,\(x^2-25+\left(x+5\right)\left(5-2x\right)\)

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

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

b,\(3x^2-6xy+3y^2-12z^2=3\left[\left(x^2-2xy+y^2\right)-4z^2\right]\)

\(=3\left[\left(x-y\right)^2-\left(2z\right)^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\)

c,\(x^3-3x^2+4x-12\)

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

d,\(x^2-y^2+4x+4=\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\)