Question

phan tich da thuc thanh nhan tu

3x^4-48

x^4-8x

x^3-6x^2+9x

Answer 1

\(3x^4-48\)

\(=\left(3x^4-6x^3\right)+\left(6x^3-12x^2\right)+\left(12x^2-24x\right)+\left(24x-48\right)\)

\(=3x^3\left(x-2\right)+6x^2\left(x-2\right)+12x\left(x-2\right)+24\left(x-2\right)\)

\(=\left(x-2\right)\left[\left(3x^3+6x^2\right)+\left(12x+24\right)\right]\)

\(=\left(x-2\right)\left[3x^2\left(x+2\right)+12\left(x+2\right)\right]\)

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

Answer 2

\(x^4-8x\)

\(=x\left(x^3-8\right)\)

\(=x\left[\left(x^3-2x^2\right)+\left(2x^2-4x\right)+\left(4x-8\right)\right]\)

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

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

Answer 3

\(x^3-6x^2+9x\)

\(=\left(x^3-3x^2\right)-\left(3x^2-9x\right)\)

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

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

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