a) x^5- 3x^4+ 3x^3- x^2
\(=x^2\left(x^3-3x^2+3x-1\right)\)
\(=x^2\left(x^3-3.x^2.1+3.x.1^2-1^3\right)\)
\(=x^2\left(x-1\right)^3\)
b)3y^2- 3z^2+ 3x^2+ 6xy
\(=3\left(y^2-z^2+x^2+2xy\right)\)
\(=3\left(\left(x^2+2.x.y+y^2\right)-z^2\right)\)
\(=3\left(\left(x+y\right)^2-z^2\right)\)
\(=3\left(x+y+z\right)\left(x+y-z\right)\)
c)x^2- 6x +5
\(=x^2-6x+9-4\)
\(=\left(x^2-2.x.3+3^2\right)-2^2\)
\(=\left(x-3\right)^2-2^2\)
=(x-3-2)(x-3+2)
=(x-5)(x-1)
d)x^2 + 5x -6
\(=x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2-\dfrac{49}{2}\)
\(=\left(x+\dfrac{5}{2}\right)^{2 }-\left(\dfrac{7}{2}\right)^2\)
\(=\left(x+\dfrac{5}{2}+\dfrac{7}{2}\right)\left(x+\dfrac{5}{2}-\dfrac{7}{2}\right)\)
=(x+6)(x-1)
e)x^2 - 5x + 4
=\(x^2-2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2-\dfrac{9}{4}\)
\(=\left(x-\dfrac{5}{2}\right)^2-\left(\dfrac{3}{2}\right)^2\)
\(=\left(x-\dfrac{5}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{5}{2}+\dfrac{3}{2}\right)\)
=(x-4)(x-1)
