Question

phân tích thành nhân tử

2x³-12x²+18x

(x²+x)²+4x²+4x-12

Answer 1

a.2x²-12x²+18x

=>2x(x²-6x+9)

=>2x(x-3)²

b.(x²+x)²+4x²+4x-12

=>x⁴+2x³+x²+4x²+4x-12

=>x⁴+2x³+5x²+4x-12

Answer 2

a) \(2x^3-12x^2+18x=2x\left(x^2+6x+9\right)=2x\left(x+3\right)^2\)

b) \(\left(x^2+x\right)^2+4x^2+4x-12\)

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

\(=\left(x^2+x\right)^2+6\left(x^2+x\right)-2\left(x^2+x\right)-12\)

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

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

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

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

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

Answer 3

2x³-12x²⁺18x=2x (x²-6x+9)=2x(x-3)²