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\(2x^2-6x+1=\left(\sqrt{2}x\right)^2-2.\sqrt{2}x.\frac{3\sqrt{2}}{2}+\left(\frac{3\sqrt{2}}{2}\right)^2-\frac{7}{2}\)
\(=\left(\sqrt{2}x-\frac{3\sqrt{2}}{2}\right)^2-\left(\frac{\sqrt{14}}{2}\right)^2\)
\(=\left(\sqrt{2}x-\frac{3\sqrt{2}}{2}+\frac{\sqrt{14}}{2}\right)\left(\sqrt{2}x-\frac{3\sqrt{2}}{2}-\frac{\sqrt{14}}{2}\right)\)
\(=\left(\sqrt{2}x+\frac{\sqrt{14}-3\sqrt{2}}{2}\right)\left(\sqrt{2}x-\frac{\sqrt{14}+3\sqrt{2}}{2}\right)\)
\(2x^2-6x+1=2\left(x^2-3x+\frac{9}{4}-\frac{7}{4}\right)=2\left[\left(x-\frac{3}{2}\right)^2-\left(\frac{\sqrt{7}}{2}\right)^2\right]=2\left(x-\frac{3}{2}-\frac{\sqrt{7}}{2}\right)\left(x-\frac{3}{2}+\frac{\sqrt{7}}{2}\right)\)
\(=2\left(x-\frac{3+\sqrt{7}}{2}\right)\left(x-\frac{3-\sqrt{7}}{2}\right)\)
\(=6x^2-2x-\left(9x-3\right)\)
\(=2x\left(3x-1\right)-3\left(3x-1\right)\)
\(=\left(2x-3\right)\left(3x-1\right)\)
\(6x^4-11x^2+3=6x^4-9x^2-2x^2+3\)
\(=3x^2\left(2x^2-3\right)-\left(2x^2-3\right)=\left(2x^2-3\right)\left(3x^2-1\right)\)
\(\left(x^2+6x\right)\left(x^2+14x+40\right)+128\)
\(=\left(x^2+6x\right)\left(x^2+14x+40\right)\)
\(=x^4+20x^3+124x^2+240x\)
\(=x^4+20x^3+124x^2+240x+128\)
\(\left(x^2+6x\right)\left(x^2+14x+40\right)+128\)
\(=x^4+14x^3+40x^2+6x^3+84x^2+240x+128\)
\(=x^4+20x^3+124x^2+240x+128\)
mk chỉ biết đến đây thôi
a) x^3 +5x^2+6x
= x^3+2x^2+3x^2+6x
=x*(x+3)*(x+2)
b) x^2-6x+8
= x^2-2x-4x+8
=(x-2)*(x-4)
c)2x^2+98+28x-8y^2
=2(x^2+14x+49-4y^2)
=2*[(x+7)^2-4y^2]
2*(x-7-2y)*(x-7+2y)
a) x2 + 2x2 + 3x2 + 6x
= x( x+2 ) + 3( x+2 )
=(x+3)(x+2)
b) x2 - 2x - 4x + 8
=x(x-2)-4(x-2)
=(x-4)(x-2)
c)
a)x2-2xy+y2-2x+2y
=(x2-2xy+y2-2x+2y+1)-1
=(x-y-1)2-1
=(x-y-2)(x-y)
b)x3-49x
=x(x2-72)
=x(x+7)(x-7)
c)x2-y2+6x+9
=(x2+6x+9)-y2
=(x+3)2-y2
=(x-y+3)(x+y+3)
d)x2-6x+5
=x2-5x-x+5
=x(x-5)-(x-5)
=(x-1)(x-5)
\(B=x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)
\(=\left(x^2+3x-1\right)^2\)