#)Giải :

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

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

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

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

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

\(x^4+2x^3+5x^2+4x-12\)

\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)

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

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

\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)

Câu 1.

Đoán được nghiệm là 2.Ta giải như sau:

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

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

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

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

\(=2x^2-6x+x-3=\left(x-3\right)\left(2x+1\right)\)

\(=2x^2-6x+x-3=2x\left(x-3\right)+\left(x-3\right)=\left(2x+1\right)\left(x-3\right)\)

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

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

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

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

\(x^4-5x^2+4=\left(x^2-4\right)\left(x^2-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)

\(16\cdot\left(2x+3\right)^2-9\cdot\left(5x-2\right)^2\\ =\left(8x+12\right)^2-\left(15x-6\right)^2\\ =\left(8x+12-15x+6\right)\left(8x+12+15x-6\right)\\ =\left(-7x+18\right)\left(23x+6\right)\)

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

e ko bt phân tích đa thức thành nhân tử nên a tham khảo linh này nha

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TL:

(5x^2 - 2x)^2+2x-5x^2-6 

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

A=2x^3-x^2+5x+3

= (2x+1).(x² - x + 3)

\(A=2x^3-x^2+5x+3\)

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

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

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