Question

Phân tích đa thức thành nhân tử \(3x^4-5x^3-18x^2-3x+5\)

Answer 1

\(3x^4-5x^3-18x^2-3x+5.\)

\(=3x^4-6x^3+x^3-15x^2-2x^2-x^2-5x+2x+5\)

\(=3x^4-6x^3-15x^2+x^3-2x^2-5x-x^2+2x+5\)

\(=\left(3x^4-6x^3-15x^2\right)+\left(x^3-2x^2-5x\right)-\left(x^2-2x-5\right)\)

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

\(=\left(x^2-2x-5\right)\left(3x^2+x-1\right)\)

Answer 2

\(3x^4-5x^3-18x^2-3x+5\)

\(=\left(3x^4-6x^3-15x^2\right)+\left(x^3-2x^2-5x\right)-\left(x^2-2x-5\right)\)

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

\(=\left(x^2-2x-5\right)\left(3x^2+x-1\right)\)