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\(x^4-5x^2+4=\left(x^2-4\right)\left(x^2-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)
\(x^3+5x^2+5x+1\)
\(=\left(x+1\right)\left(x^2+x+1\right)+5x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+6x+1\right)\)
\(4x\left(x+1\right)^2-5x^2\left(x+1\right)-4\left(x+1\right) =\left(x+1\right)\left[4x\left(x+1\right)-5x^2-4\right]=\left(x+1\right)\left(4x^2+4x-5x^2-4\right)=\left(x+1\right)\left(-x^2+4x-4\right)=-\left(x+1\right)\left(x-2\right)^2\)
\(4x\left(x+1\right)^2-5x^2\left(x+1\right)-4\left(x+1\right)\)
\(=4x\left(x^2+2x+1\right)-5x^2\left(x+1\right)-4\left(x+1\right)\)
\(=4x^3+8x^2+4x-5x^3-5x-4x-4\)
\(=-x^3+8x^2-5x-4\)
\(A=5x^3-125x=5x\left(x-5\right)\left(x+5\right)\)
\(B=x^3-8+\left(x-2\right)\left(5x+4\right)\)
\(=\left(x-2\right)\left(x^2+2x+4+5x+4\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x+4\right)\)
\(=x^2-5x+\dfrac{25}{4}-\dfrac{29}{4}\)
\(=\left(x-\dfrac{5}{2}\right)^2-\dfrac{29}{4}\)
\(=\left(x-\dfrac{5}{2}-\dfrac{\sqrt{29}}{2}\right)\left(x-\dfrac{5}{2}+\dfrac{\sqrt{29}}{2}\right)\)
\(5x^2-5x-10=5x^2+5x-10x-10=5x\left(x+1\right)-10\left(x+1\right)=\left(5x-10\right)\left(x+1\right)\)
5x2−5x−10=5x2+5x−10x−10=5x(x+1)−10(x+1)=(5x−10)(x+1)
2) \(x^4-5x^2+4\)
\(=x^4-x^2-4x^2+4\)
\(=x^2\left(x^2-1\right)-4\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2-4\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)