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#)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 - x + 6x - 3
= x(2x - 1) + 3(2x - 1)
= (x + 3)(2x - 1)
\(2x^2+5x-3\)
\(=2x^2+6x-x-3\)
\(=2x\left(x+3\right)-\left(x+3\right)\)
\(=\left(2x-1\right)\left(x+3\right)\)
\(-2x^2+5x+3\)
\(=-2x^2+6x-x+3\)
\(=-2x\left(x-3\right)-\left(x-3\right)\)
\(=\left(x-3\right)\left(-2x-1\right)\)
\(x^4-5x^2+4=\left(x^2-4\right)\left(x^2-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)
\(16\cdot\left(2x+3\right)^2-9\cdot\left(5x-2\right)^2\\ =\left(8x+12\right)^2-\left(15x-6\right)^2\\ =\left(8x+12-15x+6\right)\left(8x+12+15x-6\right)\\ =\left(-7x+18\right)\left(23x+6\right)\)
e ko bt phân tích đa thức thành nhân tử nên a tham khảo linh này nha
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\(A=2x^3-x^2+5x+3\)
\(A=\left(2x^3+x^2\right)-\left(2x^2+x\right)+\left(6x+3\right)\)
\(A=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(A=\left(2x+1\right)\left(x^2-x+3\right)\)
\(2x^2-5x+3\)
\(=2x^2-2x-3x+3\)
\(=2x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(2x-3\right)\)
\(2x^2-5x+3=2x^2-2x-3x+3\)\(=2x\left(x-1\right)-3\left(x-1\right)=\left(2x-3\right)\left(x-1\right)\)