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Câu a : \(4x^3-5x^2+6x+9\)
\(=4x^3+3x^2-8x^2-6x+12x+9\)
\(=\left(4x^3+3x^2\right)-\left(8x^2+6x\right)+\left(12x+9\right)\)
\(=x^2\left(4x+3\right)-2x\left(4x+3\right)+3\left(4x+3\right)\)
\(=\left(4x+3\right)\left(x^2-2x+3\right)\)
Câu b : \(5x^3-12x^2+14x-4\)
\(=5x^3-10x^2-2x^2+10x+4x-4\)
\(=\left(5x^3-2x^2\right)-\left(10x^2-4x\right)+\left(10x-4\right)\)
\(=x^2\left(5x-2\right)-2x\left(5x-2\right)+2\left(5x-2\right)\)
\(=\left(5x-2\right)\left(x^2-2x+2\right)\)
Câu c : \(x^3-5x^2+2x+8\)
\(=x^3+x^2-6x^2-6x+8x+8\)
\(=\left(x^3+x^2\right)-\left(6x^2+6x\right)+\left(8x+8\right)\)
\(=x^2\left(x+1\right)-6x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-6x+8\right)\)
\(=\left(x+1\right)\left[x^2-2x-4x+8\right]\)
\(=\left(x+1\right)\left[x\left(x-2\right)-4\left(x-2\right)\right]\)
\(=\left(x+1\right)\left(x-2\right)\left(x-4\right)\)
Câu d : \(4x^3+5x^2+10x-12\)
\(=4x^3+8x^2-3x^2+16x-6x-12\)
\(=\left(4x^3-3x^2\right)+\left(8x^2-6x\right)+\left(16x-12\right)\)
\(=x^2\left(4x-3\right)+2x\left(4x-3\right)+4\left(4x-3\right)\)
\(=\left(4x-3\right)\left(x^2+2x+4\right)\)
`#3107`
`a.`
`4x^2 - 6x = 2x(2x - 3)`
`b.`
`9x^4y^3 + 3x^2y^4 = 3x^2y^2(3x^2y + y^2)`
`c.`
`x^3 - 2x^2 + 5x`
`= x(x^2 - 2x + 5)`
a) 4x² - 6x
= 2x(2x - 3)
b) 9x⁴y³ + 3x²y⁴
= 3x²y³(3x² + 3y)
c) x³ - 2x² + 5x
= x(x² - 2x + 5)
\(=\dfrac{6x}{\left(x-3\right)\left(x+3\right)}-\dfrac{9+5x}{x-3}+\dfrac{x}{x+3}\)
\(=\dfrac{6x-\left(5x+9\right)\left(x+3\right)+x^2-3x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{x^2+3x-5x^2-15x-9x-27}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{-4x^2-21x-27}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{-\left(4x^2+12x+9x+27\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{-4x-9}{x-3}\)
\(5x^3-5x^2y-10x^2+10xy=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-2\right)\left(x-y\right)\)
\(x^3+5x^2-6x\)
\(=x^3+6x^2-x^2-6x\)
\(=x^2.\left(x+6\right)-x.\left(x+6\right)\)
\(=\left(x^2-x\right).\left(x+6\right)\)
\(x^3+5x^2-6x\)
\(=x\left(x^2+5x-6\right)\)
\(=x\left(x^2+6x-x-6\right)\)
\(=x\left[x\left(x+6\right)-\left(x+6\right)\right]\)
\(=x\left(x+6\right)\left(x-1\right)\)