a: \(x^2+x-2023\cdot2024\)
\(=x^2+2024x-2023x-2023\cdot2024\)
\(=x\left(x+2024\right)-2023\left(x+2024\right)\)
\(=\left(x+2024\right)\left(x-2023\right)\)
c: \(x^3-5x^2+7x+13\)
\(=x^3+x^2-6x^2-6x+13x+13\)
\(=x^2\left(x+1\right)-6x\left(x+1\right)+13\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-6x+13\right)\)
d: \(2x^3-3x^2-4x+4\)
\(=2x^3-4x^2+x^2-4x+4\)
\(=2x^2\left(x-2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(2x^2+x-2\right)\)
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