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a)\(x^2-5x+4\)
\(=x^2-x-4x+4\)
\(=x\left(x-1\right)-4\left(x-1\right)\)
=\(\left(x-1\right)\left(x-4\right)\)
b)\(4x^2-4x-3\)
\(=4x^2+2x-6x-3\)
\(=2x\left(2x+1\right)-3\left(2x+1\right)\)
\(=\left(2x-3\right)\left(2x+1\right)\)
a) \(x^2-5x+4\)
\(=x^2-4x-x+4\)
\(=\left(x^2-4x+4\right)-x\)
\(=\left(x-2\right)^2-x\)
\(=\left(x-2\right)^2-\left(\sqrt{x}\right)^2\)
\(=\left(x-2-\sqrt{x}\right)\left(x-2+\sqrt{x}\right)\)
b) \(4x^2-4x-3\)
\(=4x^2-4x+1-4\)
\(=\left(2x+1\right)^2-2^2\)
\(=\left(2x+1-2\right)\left(2x+1+2\right)\)
\(=\left(2x-1\right)\left(2x+3\right)\)
x6+3x4y2-8x3y3+3x2y4+y6= x6+3x4y2+3x2y4+y6-8x3y3=(x2+y2)3-(2xy)3
= (x2+y2-2xy)[(x2+y2)2+2xy(x2+y2)+(2xy)2]= (x-y)2(x4+6x2y2+y4+2x3y+2xy3)
(x2+y2-5)2-4x2y2-16xy-16=(x2+y2-5)2-(4x2y2+16xy+16)=(x2+y2-5)2-(2xy+4)2
=(x2+y2-5+2xy+4)(x2+y2-5-2xy-4)=(x2+2xy+y2-1)(x2-2xy+y2-9)=[(x+y)2-1][(x-y)2-32]=(x+y-1)(x+y+1)(x-y-3)(x-y+3)
x4+324=x4+36x2+324-36x2=(x2+18)2-(6x)2=(x2+18-6x)(x2+18+6x)
\(a,x^2-5x+4=x^2-4x-x+4=x\left(x-4\right)-\left(x-4\right)=\left(x-4\right)\left(x-1\right)\)
\(b,4x^2-4x-3=4x^2-2.2x.1+1-3-1=\left(2x-1\right)^2-4=\left(2x-1-2\right)\left(2x-1+2\right)=\left(2x-3\right)\left(2x+1\right)\)
4x3+4x4−x2−x
=4x3(x+1)−x(x+1)
=(x+1)(4x3−1)
ĐÂY NHÉ. T.I.C.K MÌNH VỚI
\(x^4+2x^2-24=x^4-4x^2+2x^2-24+4x^2=\left(x^4-4x^2\right)+\left(6x^2-24\right)\)
\(=x^2\left(x^2-4\right)+6\left(x^2-4\right)=\left(x^2+6\right)\left(x^2-4\right)=\left(x^2+6\right)\left(x-2\right)\left(x+2\right)\)
a, x^5+x^4+x^3-x^3-x²-x+x²+x+1
= x^3(x²+x+1)-x(x²+x+1)+1(x²+x+1)
= (x²+x+1).(x³-x²+1)
x2-4x+3
x2-x-3x-3
=(x2-x)-(3x-3)
=x(x-1) - 3(x-1)
=(x-3)(x-1)
x4+4=x4+4x2+4-4x2
=(x2+2)2-4x2
=(x2-2x+2)(x2+2x+2)
x4+x4=x4+4x2+4-4x2
=(x2+2)2-4x2
=(x2-2x+2) (x2+2x+2)