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1, = 6(x^2 .y -z^2 +10x+25 )
2, = x^2 -2x-9x+18
= x(x-2)-9(x-2)
= (x-9)(x-2)
\(xy\left(x-y\right)+yz\left(y-z\right)+zx\left(z-x\right)=x^2y-xy^2+y^2z-yz^2+z^2z-zx^2=x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(z-y\right)\)
\(x^2\left(y-z\right)-y^2\left(x-z\right)-z^2\left(y-z\right)=\left(y-z\right)\left(x-z\right)\left(x+z\right)-y^2\left(x-z\right)=\left(x-z\right)\left(xy-yz-zx-z^2-y^2\right)\)
t cx k bt có đúng hay k đâu nha, nhớ xem kĩ lại
a) x3 -2x2 +5x-4
=x3-x2-x2+x+4x-4
=x2(x-1)-x(x-1)+4(x-1)
=(x2-x+4)(x-1)
b) x3-x2+x+3
=x3+x2-2x2-2x+3x+3
=x2(x+1) -2x(x+1)+3(x+1)
=(x2-2x+3)(x+1)
c) 6x3+x2+x+1
=6x3+ 3x2-2x2-x+2x+1
=6x2(x+\(\frac{1}{2}\)) - 2x(x+\(\frac{1}{2}\)) +2(x+\(\frac{1}{2}\))
=(6x2-2x+2) (x+\(\frac{1}{2}\))
=2( 3x2-x+1) (x+\(\frac{1}{2}\))
d) 4x3 + 6x2+4x+1
= 4x3+2x2+4x2+2x+2x+1
= 4x2(x+\(\frac{1}{2}\))+ 4x(x+\(\frac{1}{2}\))+2(x+\(\frac{1}{2}\))
= 2(2x2 +2x+1)( x+\(\frac{1}{2}\))
e) x6 -9x3+8
a)\(-6x^3+18^2+60x\)
\(=6x.-x^2+6x.3x+6x.10\)
=\(6x\left(-x^2+3x+10\right)\)
b)\(x^7+x^2+1\)
=\(\left(x^7-x\right)+\left(x^2+x+1\right)\)
=\(x\left(x^6-1\right)+\left(x^2+x+1\right)\)
\(=x\left(x^3-1\right).\left(x^3+1\right)+\left(x^2+x+1\right)\)
=\(x\left(x-1\right).\left(x^2+x+1\right).\left(x^3+1\right)+\left(x^2+x+1\right)\)
=\(\left(x^2+x+1\right).\left[x.\left(x-1\right).\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right).\left[\left(x^2-x\right).\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right).\left(x^5+x^4+x^2-x+1\right)\)
Bạn học tốt nhé!
c)\(x^{10}+x^5+1\)
\(=x^{10}+x^9-x^9+x^8-x^8+x^7-x^7+x^6-x^6+\)\(x^5+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-x+1\)
=\(\left(x^{10}+x^9+x^8\right)-\left(x^9+x^8+x^7\right)+\left(x^7+x^6+x^5\right)\)
\(-\left(x^6+x^5+x^4\right)+\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)\)
\(+\left(x^2+x+1\right)\)
=\(x^8\left(x^2+x+1\right)-x^7\left(x^2+x+1\right)+x^5\left(x^2+x+1\right)\)\(-x^4\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)\)
\(+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right).\left(x^8-x^7+x^5-x^4+x^3-x+1\right)\)
Lộn xộn quá ha, chúc bạn học thật giỏi!