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\(\left(x^2+4x-3\right)^2-5x.\left(x^2+4x-3\right)+6x^2\)
\(=\left[\left(x^2+4x-3\right)^2-2.\left(x^2+4x-3\right).2,5x+\left(2,5x\right)^2\right]-\left(0,5x\right)^2\)
\(=\left(x^2+4x-3-2,5x\right)^2-\left(0,5x\right)^2\)
\(=\left(x^2+4x-3-2,5x-0,5x\right).\left(x^2-4x-3-2,5x+0,5x\right)\)
\(=\left(x^2+x-3\right).\left(x^2+2x-3\right)\)
Tham khảo nhé~
\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
1 )
=x3-2x2+6x2-12x+5x-10
=x2(x-2)+6x(x-2)+5(x-2)
=(x-2)(x2+6x+5)
=(x-2)(x2+x+5x+5)
=(x-2)[x(x+1)+5(x+1)]
=(x-2)(x+1)(x+5)
toàn mũ lớn hơn 3 khó làm quá!!!! >.<
653645645645645676746784734746856876897684737547
4x4 + 4x3 + 5x2 + 2x +1
= (4x4 + 4x3 + x2 ) + ( 2x2 + 1 ) + 1
= x2(2x + 1 )2 + 2x(2x + 1) +1
= (x(2x + 1 ) + 1)2
= (2x + x + 1)2
4x4+4x3+5x2+2x+1
=(4x4+4x3+x2) + (2x2+1) +1
= x2(2x+1)2 + 2x(2x+1) +1
= (x(2x+1)+1)2
=(2x2+x+1)2
a)\(x^5-x=x\left(x^4-1\right)=x\left(x^2-1\right)\left(x^2+1\right)=x\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\)
b)\(3x^2+5x-2=3x^2+6x-x-2=3x\left(x+2\right)-\left(x+2\right)=\left(3x-1\right)\left(x+2\right)\)
c)\(4x^3+14x^2+6x=2x\left(2x^2+7x+3\right)=2x\left(2x^2+6x+x+3\right)\)
\(=2x\left[2x\left(x+3\right)+\left(x+3\right)\right]=2x\left(x+3\right)\left(2x+1\right)\)
\(x^5-x=x\left(x^4-1\right)\)
\(=x\left(x^2-1\right)\left(x^2+1\right)\)
\(=x\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\)
\(x^5-5x^3+4x=x\left(x^4-5x^2+4\right)=x\left(x^4-x^2-4x^2+4\right)\)
\(=x\left[x^2\left(x^2-1\right)-4\left(x^2-1\right)\right]=x\left(x^2-1\right)\left(x^2-4\right)\)
\(=x\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
\(x^5-5x^3+4x=x^5-4x^3-x^3+\) \(4x\)
\(=\) \(x^3.\left(x^2-4\right)-x.\left(x^2-4\right)\)
\(=\left(x^3-x\right)\left(x^2-4\right)\)
\(=x\left(x^2-1\right)\left(x^2-4\right)\)
\(=x\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)