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\(a,x^2-5x+4=x^2-4x-x+4=x\left(x-4\right)-\left(x-4\right)=\left(x-4\right)\left(x-1\right)\)
\(b,4x^2-4x-3=4x^2-2.2x.1+1-3-1=\left(2x-1\right)^2-4=\left(2x-1-2\right)\left(2x-1+2\right)=\left(2x-3\right)\left(2x+1\right)\)
\(x^4+2x^2-24=x^4-4x^2+2x^2-24+4x^2=\left(x^4-4x^2\right)+\left(6x^2-24\right)\)
\(=x^2\left(x^2-4\right)+6\left(x^2-4\right)=\left(x^2+6\right)\left(x^2-4\right)=\left(x^2+6\right)\left(x-2\right)\left(x+2\right)\)
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
a) 2x3-5x2+8x-3
=2x3-x2-4x2+2x+6x-3
=x2(2x-1)-2x(2x-1)+3(2x-1)
=(2x-1)(x2-2x+3)
a,2x3-5x2+8x-3
=2x3-x2-4x2+2x+6x-3
=x2(2x-1)-2x(2x-1)+3(2x-1)
=(2x-1)(x2-2x+3)
a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
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
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) \(4x^2-4x-3\)
\(=4x^2-4x+1-4\)
\(=\left(2x+1\right)^2-2^2\)
\(=\left(2x+1-2\right)\left(2x+1+2\right)\)
\(=\left(2x-1\right)\left(2x+3\right)\)