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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
ta có :4.x^4 +4.x^3 +5.x^2 +2x+1=(2.x^2)^2 +2.2.(x^2).x +x^2 +4.x^2 +2x +1
=(2.x^2 +x)^2 +2.(2x^2 +x) .1 +1
=(2.x^2 +x +1)^2
\(x^4+2x^3-4x-4\)
\(=x^4+2x^3-4x-4+2x^2-2x^2\)
\(=\left(x^4-2x^2\right)+\left(2x^3-4x\right)+\left(2x^2-4\right)\)
\(=x^2\left(x^2-2\right)+2x\left(x^2-2\right)+2\left(x^2-2\right)\)
\(=\left(x^2+2x+2\right)\left(x^2-2\right)\)
\(=\left(x^2+2x+2\right)\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
\(x^4-2x^3+2x-1\)
\(=\left(x^4-3x^3+3x^2-x\right)+\left(x^3-3x^2+3x-1\right)\)
\(=x\left(x-1\right)^3+\left(x-1\right)^3\)
\(=\left(x+1\right)\left(x-1\right)^3\)
d) x3-4x2-9x+36
=x2(x-4)-9(x-4)
=(x-4)(x2-9)
=(x-4)(x+3)(x-3)
e)(x+1)3+(2x-1)3
=x3+3x2+3x+1+8x3-12x2+6x-1
=9x3-9x2+9x
=9x(x2-x+1)
g)x3+3x2-4x-12
=x2(x+3)-4(x+3)
=(x+3)(x2-4)
=(x+3)(x+2)(x-2)
h) x3-4x2+4x-1
=x3-1-4x2+4x
=(x-1)(x2+x+1)-4x(x-1)
=(x-1)(x2+x+1-4x)
=(x-1)(x2-3x+1)