Question

[ran mori]

phân tích đa thức thành nhân tử:

x^3-19x-30

Answer 1

[Ben 10]

x^3-19x-30 
=x^3-25x+6x-30 
=x(x^2-25)+6(x-5) 
=x(x+5)(x-5)+6(x-5) 
=(x-5)(x^2+5x+6) 
=(x-5)(x^2+2x+3x+6) 
=(x-5)[x(x+2)+3(x+2)] 
=(x-5)(x+2)(x+3)

Answer 2

[Lê Anh Tú]

\(x^3-19x-30=x^3+2x^2-2x^2-4x-15x-30\)

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

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

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