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a: ĐKXD: x<>0
\(\dfrac{14x^3+12x^2-14x}{2x}=\left(x+2\right)\left(3x-4\right)\)
=>\(\dfrac{2x\left(7x^2+6x-7\right)}{2x}=\left(x+2\right)\left(3x-4\right)\)
=>\(7x^2+6x-7=3x^2-4x+6x-8\)
=>\(7x^2+6x-7=3x^2+2x-8\)
=>\(4x^2+4x+1=0\)
=>\(\left(2x+1\right)^2=0\)
=>2x+1=0
=>x=-1/2(nhận)
b: \(\left(4x-5\right)\left(6x+1\right)-\left(8x+3\right)\left(3x-4\right)=15\)
=>\(24x^2+4x-30x-5-\left(24x^2-32x+9x-12\right)=15\)
=>\(24x^2-26x-5-24x^2+23x+12=15\)
=>-3x+7=15
=>-3x=8
=>\(x=-\dfrac{8}{3}\)
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\(2x^2-3x-2\)
\(=2x^2-4x+x-2\)
\(=2x\left(x-2\right)+\left(x-2\right)\)
\(=\left(x-2\right)\left(2x+1\right)\)
\(3x^2+x-2\)
\(=3x^2+3x-2x-2\)
\(=3x\left(x+1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-2\right)\)
\(4x^2-7x-2\)
\(=4x^2-8x+x-2\)
\(=4x\left(x-2\right)+x-2\)
\(=\left(x-2\right)\left(4x+1\right)\)
\(4,4x^2+5x-6=4x^2+8x-3x-6\)
\(=4x\left(x+2\right)-3\left(x+2\right)=\left(4x-3\right)\left(x+2\right)\)
\(5,\) \(4x^2+15x+9=4x^2+12x+3x+9\)
\(=4x\left(x+3\right)+3\left(x+3\right)\)
\(=\left(4x+3\right)\left(x+3\right)\)
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\(3x^3-14x^2+4x+3\)
\(=\left(3x^3-15x^2+9x\right)+\left(x^2-5x+3\right)\)
\(=3x\left(x^2-5x+3\right)+\left(x^2-5x+3\right)\)
\(=\left(3x+1\right)\left(x^2-5x+3\right)\)
3x^3 - 14x^2 + 4x + 3
= (3x^3+x^2) - 15^2- 5x+ 9x+ 3
= x^2(3x+1)- 5x(3x+1)+ 3(3x+1)
= (x^2- 5x+ 3)(3x+1)
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Bài 1.
a)
\((x-2)(2x-1)-(2x-3)(x-1)-2\\=2x^2-x-4x+2-(2x^2-2x-3x+3)-2\\=2x^2-5x+2-(2x^2-5x+3)-2\\=2x^2-5x+2-2x^2+5x-3-2\\=(2x^2-2x^2)+(-5x+5x)+(2-3-2)\\=-3\)
b)
\(x(x+3y+1)-2y(x-1)-(y+x+1)x\\=x^2+3xy+x-2xy+2y-xy-x^2-x\\=(x^2-x^2)+(3xy-2xy-xy)+(x-x)+2y\\=2y\)
Bài 2.
a)
\((14x^3+12x^2-14x):2x=(x+2)(3x-4)\\\Leftrightarrow 14x^3:2x+12x^2:2x-14x:2x=3x^2-4x+6x-8\\ \Leftrightarrow 7x^2+6x-7=3x^2+2x-8\\\Leftrightarrow (7x^2-3x^2)+(6x-2x)+(-7+8)=0\\\Leftrightarrow 4x^2+4x+1=0\\\Leftrightarrow (2x)^2+2\cdot 2x\cdot 1+1^2=0\\\Leftrightarrow (2x+1)^2=0\\\Leftrightarrow 2x+1=0\\\Leftrightarrow 2x=-1\\\Leftrightarrow x=\frac{-1}2\)
b)
\((4x-5)(6x+1)-(8x+3)(3x-4)=15\\\Leftrightarrow 24x^2+4x-30x-5-(24x^2-32x+9x-12)=15\\\Leftrightarrow 24x^2-26x-5-(24x^2-23x-12)=15\\\Leftrightarrow 24x^2-26x-5-24x^2+23x+12=15\\\Leftrightarrow -3x+7=15\\\Leftrightarrow -3x=8\\\Leftrightarrow x=\frac{-8}3\\Toru\)
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a, \(3x^3-4x^2+5x-4\)
\(=3x^3-3x^2-x^2+x+4x-4\)
\(=3x^2\left(x-1\right)-x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(3x^2-x+4\right)\left(x-1\right)\)
b, \(4x^3-3x^2+5x-21\)
\(=4x^3-7x^2+4x^2-7x+12x-21\)
\(=x^2\left(4x-7\right)+x\left(4x-7\right)+3\left(4x-7\right)\)
\(=\left(x^2+x+3\right)\left(4x-7\right)\)
c, \(3x^3+8x^2+14x+15\)
\(=3x^3+5x^2+3x^2+5x+9x+15\)
\(=x^2\left(3x+5\right)+x\left(3x+5\right)+3\left(3x+5\right)\)
\(=\left(x^2+x+3\right)\left(3x+5\right)\)
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