Question

phân tích đa thức sau thành nhân tử x^4-3x^3-x+3

Answer 1

\(x^4-3x^3-x+3\)

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

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

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

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

\(=\left[x^3-2x^2-2x-3\right]\left(x-1\right)\)

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

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

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

Answer 2

\(x^4-3x^3-x+3\)

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

= \(\left(x-1\right)\left(x-3\right)\)

Answer 3

x⁴ - 3x³ - x + 3

= (x⁴ - 3x³) - (x + 3)

= x³ (x - 3) - (x - 3)

= (x - 3)(x³ - 1)

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