a) $3x^2 – 6x + 9x^2$
= $3x (x -2 +3x)$
.
b) $10x(x – y) – 6y(y – x)$
= $10x(x – y) + 6y(x - y)$
=$( x - y) ( 10x + 6y)$
.
c) $3x^2 + 5y – 3xy – 5x$
= $(3x^2 - 3xy) + (5y - 5x)$
= $3x(x-y) + 5(y-x)$
= $3x(x-y) - 5(x-y)$
=$(x-y)(3x-5)$
.
d) $3y^2 – 3z^2 + 3x^2 + 6xy$
= $3( y^2 - z^2 + x^2 +2xy)$
.
e. $16x^3 + 54y^3 = 2 (8x^3 + 27y^3)$
.
f. $x^2 – 25 – 2xy + y^2$
=$( x^2 – 2xy + y^2) - 5^2$
= $(x-y)^2 - 5^2$
=$(x-y-5)(x-y+5)$
.
g) $x^5 – 3x^4 + 3x^3 – x^2.$
= $x^2(x^3 - 3x^2 +3x -1)$
.
5) $3x^3y^2 : x^2$
= $3xy^2$
.
b) $(x^5 + 4x^3 – 6x^2) : 4x^2 = (1/4)x^3 + x - 3/2$
.
c) $(x^3 – 8) : (x^2 + 2x + 4)$
= $(x-2)(x^2+2x+4) : (x^2 + 2x + 4)$
=$x-2$
.
d) $(3x^2 – 6x) : (2 – x)$
=$-3x(2-x) : (2 – x)$
= $-3x$
.
e. $(x^3 + 2x^2 – 2x – 1) : (x^2 + 3x + 1)$
= $(x-1)(x^2 + 3x + 1) : (x^2 + 3x + 1)$
= $x-1$