[tex]\displaystyle\\
14)\\
a)~3x^3+6x^2+3x=3x(x^2+2x+1)=3x(x+1)^2\\\\
b)~4x(x+1)-3(x+1)=(x+1)(4x-3)\\\\
c)\\
(x+1)^2-9=(x+1)^2-3^2=(x+1+3)(x+1-3)=(x+4)(x-2)\\\\
d)~4x^2-(x-1)^2=(2x)^2-(x-1)^2=(2x+(x-1))(2x-(x-1))=\\
=(2x+x-1)(2x-x+1))=(3x-1)(x+1)\\\\
e)~x^2+6x+8 = x^2 +2x+4x+8=\\
=x(x+2)+4(x+2)=(x+2)(x+4)\\\\
f)~x^2-9x+14=x^2-2x-7x+14=\\
=x(x-2)-7(x-2)=(x-2)(x-7)\\\\
g)~x^3+3x^2-4x-12=x^2(x+3)-4(x+3)=\\
=(x+3)(x^2-4)=(x+3)(x^2-2^2)=(x+3)(x+2)(x-2)
[/tex]
[tex]\displaystyle\\
h)~x^3+2x^2-9x-18=x^2(x+2)-9(x+2)=\\
=(x+2)(x^2-9)=(x+2)(x^2-3^2)=(x+2)(x+3)(x-3)\\\\
i)~x^2-6x-16=x^2+2x-2x-6x-16=x^2+2x-8x-16=\\
=x(x+2)-8(x+2)=(x+2)(x-8)[/tex]
